Question

How do you write the first five terms of the sequence ${a_n} = {2^n}$?

Answer 1

Here, we will find the terms in a sequence by using the given ${n^{th}}$ term of an AP i.e. the given equation. Then we will substitute different values of $n$, to find the required consecutive terms. An arithmetic sequence is a sequence of numbers such that the common difference between any two consecutive numbers is a constant.

Complete Step by Step Solution:
The equation is the ${n^{th}}$ term of an AP.
First, we will find the first term of the sequence by substituting $n = 1$ in ${a_n} = {2^n}$. Therefore, we get
${a_1} = {2^1}$
Applying the exponent on the terms, we get
$\Rightarrow {a_1} = 2$
Now, we will find the second term of the sequence by substituting $n = 2$ in ${a_n} = {2^n}$ , we get
${a_2} = {2^2}$
Applying the exponent on the terms, we get
$\Rightarrow {a_2} = 4$
Now, we will find the third term of the sequence by substituting $n = 3$ in ${a_n} = {2^n}$, we get
${a_3} = {2^3}$
Applying the exponent on the terms, we get
$\Rightarrow {a_3} = 8$
We will find the fourth term of the sequence by substituting $n = 4$ in ${a_n} = {2^n}$, we get
${a_4} = {2^4}$
Applying the exponent on the terms, we get
$\Rightarrow {a_4} = 16$
Now, we will find the fifth term of the sequence by substituting $n = 5$ in ${a_n} = {2^n}$, we get
${a_5} = {2^5}$
Applying the exponent on the terms, we get
$\Rightarrow {a_5} = 32$

Therefore, the first five terms of the sequence ${a_n} = {2^n}$ are $2,4,8,16,32$.

Note:
We know that a sequence of real numbers is defined as an arrangement or a list of real numbers in a specific order. We should know that if a sequence has only a finite number of terms then it is called a finite sequence and if a sequence has infinitely many terms, then it is called an infinite sequence. If we are given a general term of a sequence and then we will be able to find any particular term of the sequence directly.