Question

How do you write the first six terms of the sequence ${a_n} = n + 1$?

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 formula of an AP.
First, we will find the first term of the sequence by substituting $n = 1$ in ${a_n} = n + 1$. Therefore, we get
${a_1} = 1 + 1$
Adding the terms, we get
$\Rightarrow {a_1} = 2$
Now, we will find the second term of the sequence by substituting $n = 2$ in ${a_n} = n + 1$, so we get
${a_2} = 2 + 1$
Adding the terms, we get
$\Rightarrow {a_2} = 3$
Now, we will find the third term of the sequence by substituting $n = 3$ in ${a_n} = n + 1$.
${a_3} = 3 + 1$
Adding the terms, we get
$\Rightarrow {a_3} = 4$
We will now find the fourth term of the sequence by substituting $n = 4$ in ${a_n} = n + 1$. So, we get
${a_4} = 4 + 1$
Adding the terms, we get
$\Rightarrow {a_4} = 5$
Now, we will find the fifth term of the sequence by substituting $n = 5$ in ${a_n} = n + 1$, we get
${a_5} = 5 + 1$
Adding the terms, we get
$\Rightarrow {a_5} = 6$
We will now find the sixth term of the sequence by substituting $n = 6$ in ${a_n} = n + 1$, we get
${a_6} = 6 + 1$
Adding the terms, we get
$\Rightarrow {a_6} = 7$

Therefore, the first six terms of the sequence ${a_n} = n + 1$ are $2,3,4,5,6,7$.

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.