Question

If the \[{n^{th}}\] term is an A.P in 2n+5, then its first term is
A. 3
B. 5
C. 7
D. 9

Answer 1

Hint: This is a very basic question of arithmetic progression we will use the value and the properties of \[{a_n}\] which is also the \[{n^{th}}\] term of an A.P to find the value of the first term.

Complete step by step answer:
We know that \[{a_n} = a + (n - 1)d\& {a_n} = 2n + 5\]
Where \[{a_n}\] is the \[{n^{th}}\] , a is the first term and d is the common difference and n is the term we are trying to find out between two terms of an AP.
We are given that \[{a_n} = 2n + 5\]
So in place of n if we put 1 then we should be able to gain the value of the \[{1^{st}}\] term
As we know that \[{a_n} = 2n + 5\]
Now replacing the value of \[n = 1\]
We will get
\[\begin{array}{l}
\therefore a = {a_1} = 2 \times 1 + 5\\
 = 2 + 5\\
 = 7
\end{array}\]
Hence the first term is 7 and option C is the correct answer here.

Note:
It must be noted that the \[{n^{th}}\] term of an A.P is given by \[{a_n} = a + (n - 1)d\] and the sum of n terms of an AP is given by \[{S_n} = \dfrac{n}{2}\left\{ {2a + (n - 1)d} \right\}\] . also note that \[{S_n} = \dfrac{n}{2}\left\{ {a + {a_n}} \right\}\].