NCERT Solutions for Class 11 Maths Chapter 9 – Sequences and Series Ex 9.1
Page No 180:
Question 1:
Write the first five terms of the sequences whose nth term is ![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/169/5421/chapter%209_html_f556abe.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/169/5421/chapter%209_html_f556abe.gif)
Answer:
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/169/5421/chapter%209_html_f556abe.gif)
Substituting n = 1, 2, 3, 4, and 5, we obtain
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/169/5421/chapter%209_html_10c33c35.gif)
Therefore, the required terms are 3, 8, 15, 24, and 35.
Question 2:
Write the first five terms of the sequences whose nth term is ![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/169/5422/chapter%209_html_m4ccefe05.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/169/5422/chapter%209_html_m4ccefe05.gif)
Answer:
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/169/5422/chapter%209_html_m4ccefe05.gif)
Substituting n = 1, 2, 3, 4, 5, we obtain
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/169/5422/chapter%209_html_50a3fda2.gif)
Therefore, the required terms are
.
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/169/5422/chapter%209_html_794f5c97.gif)
Question 3:
Write the first five terms of the sequences whose nth term is an = 2n
Answer:
an = 2n
Substituting n = 1, 2, 3, 4, 5, we obtain
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/169/5423/chapter%209_html_5a6df541.gif)
Therefore, the required terms are 2, 4, 8, 16, and 32.
Question 4:
Write the first five terms of the sequences whose nth term is ![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/169/5594/Chapter%209_html_15221dac.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/169/5594/Chapter%209_html_15221dac.gif)
Answer:
Substituting n = 1, 2, 3, 4, 5, we obtain
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/169/5594/Chapter%209_html_4019a72b.gif)
Therefore, the required terms are
.
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/169/5594/Chapter%209_html_mfa0ca6d.gif)
Question 5:
Write the first five terms of the sequences whose nth term is ![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/169/5595/Chapter%209_html_459c0493.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/169/5595/Chapter%209_html_459c0493.gif)
Answer:
Substituting n = 1, 2, 3, 4, 5, we obtain
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/169/5595/Chapter%209_html_m71955e23.gif)
Therefore, the required terms are 25, –125, 625, –3125, and 15625.
Question 6:
Write the first five terms of the sequences whose nth term is ![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/169/5596/Chapter%209_html_m139cb272.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/169/5596/Chapter%209_html_m139cb272.gif)
Answer:
Substituting n = 1, 2, 3, 4, 5, we obtain
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/169/5596/Chapter%209_html_748ef08a.gif)
Therefore, the required terms are![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/169/5596/Chapter%209_html_2c510480.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/169/5596/Chapter%209_html_2c510480.gif)
Question 7:
Find the 17th term in the following sequence whose nth term is![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/169/5597/Chapter%209_html_104e0b82.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/169/5597/Chapter%209_html_104e0b82.gif)
Answer:
Substituting n = 17, we obtain
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/169/5597/Chapter%209_html_79c44e87.gif)
Substituting n = 24, we obtain
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/169/5597/Chapter%209_html_589a83d9.gif)
Question 8:
Find the 7th term in the following sequence whose nth term is![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/169/5598/Chapter%209_html_m645a83cc.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/169/5598/Chapter%209_html_m645a83cc.gif)
Answer:
Substituting n = 7, we obtain
![](https://img-nm.mnimgs.com/img/study_content/editlive_ncert/90/2012_04_09_16_59_00/mathmlequation2664305987458295483.png)
Question 8:
Find the indicated terms in each of the sequences in Exercises 7 to 10 whose nth terms are :
an = n22n ; a7
Answer:
Here,
an=n22n.
Substituting n = 7, we obtain
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/169/5428/chapter%209_html_m304b19e8.gif)
Question 9:
Find the 9th term in the following sequence whose nth term is![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/169/5599/Chapter%209_html_m63c6aa98.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/169/5599/Chapter%209_html_m63c6aa98.gif)
Answer:
Substituting n = 9, we obtain
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/169/5599/Chapter%209_html_m56e4a1d5.gif)
Question 10:
Find the 20th term in the following sequence whose nth term is ![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/169/5600/Chapter%209_html_m6721ac9.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/169/5600/Chapter%209_html_m6721ac9.gif)
Answer:
Substituting n = 20, we obtain
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/169/5600/Chapter%209_html_m4de0ac67.gif)
Page No 181:
Question 11:
Write the first five terms of the following sequence and obtain the corresponding series:
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/169/5431/chapter%209_html_m13058db2.gif)
Answer:
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/169/5431/chapter%209_html_m13058db2.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/169/5431/chapter%209_html_6d1fc392.gif)
Hence, the first five terms of the sequence are 3, 11, 35, 107, and 323.
The corresponding series is 3 + 11 + 35 + 107 + 323 + …
Question 12:
Write the first five terms of the following sequence and obtain the corresponding series:
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/169/5432/chapter%209_html_7c8c8d9.gif)
Answer:
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/169/5432/chapter%209_html_7c8c8d9.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/169/5432/chapter%209_html_m27af2a86.gif)
Hence, the first five terms of the sequence are![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/169/5432/chapter%209_html_m50f78fa0.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/169/5432/chapter%209_html_m50f78fa0.gif)
The corresponding series is![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/169/5432/chapter%209_html_m2a48d4b2.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/169/5432/chapter%209_html_m2a48d4b2.gif)
Question 13:
Write the first five terms of the following sequence and obtain the corresponding series:
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/169/5433/chapter%209_html_m36227c66.gif)
Answer:
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/169/5433/chapter%209_html_m36227c66.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/169/5433/chapter%209_html_5b173a0e.gif)
Hence, the first five terms of the sequence are 2, 2, 1, 0, and –1.
The corresponding series is 2 + 2 + 1 + 0 + (–1) + …
Question 14:
The Fibonacci sequence is defined by
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/169/5601/Chapter%209_html_613ee0fc.gif)
Find ![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/169/5601/Chapter%209_html_4a3d1d91.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/169/5601/Chapter%209_html_4a3d1d91.gif)
Answer:
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/169/5601/Chapter%209_html_m1082c6c0.gif)