Write first five terms of sequences whose n^{t h} term is a_{n}=2^{n}

English

Gujarati

Hindi

8. Sequences and Series

easy

Write the first five terms of the sequences whose $n^{t h}$ term is $a_{n}=2^{n}$

A

$2,4,8,16,32$

B

$2,4,8,16,32$

C

$2,4,8,16,32$

D

$2,4,8,16,32$

Solution

$a_{n}=2^{n}$

Substituting $n=1,2,3,4,5,$ we obtain

$a_{1}=2^{1}=2$

$a_{2}=2^{2}=4$

$a_{3}=2^{3}=8$

$a_{4}=2^{4}=16$

$a_{5}=2^{5}=32$

Therefore, the required terms are $2,4,8,16$ and $32$

Standard 11

Mathematics

Share

Similar Questions

If $a_m$ denotes the mth term of an $A.P.$ then $a_m$ =

easy

Write the first five terms of the following sequence and obtain the corresponding series :

$a_{1}=-1, a_{n}=\frac{a_{n-1}}{n}, n\, \geq\, 2$

medium

For a series $S = 1 -2 + 3\, -\, 4 … n$ terms,

Statement $-1$ : Sum of series always dependent on the value of $n$ , i.e. whether it is even or odd.

Statement $-2$ : Sum of series is $-\frac {n}{2}$ when value of $n$ is any even integer

normal

Let $s _1, s _2, s _3, \ldots \ldots, s _{10}$ respectively be the sum to 12 terms of 10 A.P.s whose first terms are $1,2,3, \ldots, 10$ and the common differences are $1,3,5, \ldots, 19$ respectively. Then $\sum \limits_{i=1}^{10} s _{ i }$ is equal to

hard

(JEE MAIN-2023)

Shamshad Ali buys a scooter for $Rs$ $22000 .$ He pays $Rs$ $4000$ cash and agrees to pay the balance in annual instalment of $Rs$ $1000$ plus $10 \%$ interest on the unpaid amount. How much will the scooter cost him?

hard