Question

Find the number of terms in the Arithmetic Progression $2,7,12,....97$.

• A. 20
• B. 19
• C. 18
• D. 21

Answer 1

The correct option is A 20

Given AP is $2,7,12,....97$.

First term, $a=2$

Common difference, $d=7-2=12-7=5$

$n^{th}term,a_n=97$

Using formula $a_n=a+(n-1)d$ to find $n^{th}$ term of arithmetic progression, we get

$\Rightarrow a_n=a+(n-1)d$

$\Rightarrow 97=2+(n-1)5$

$\Rightarrow 95=5n-5$

$\Rightarrow 100=5n$

$\Rightarrow n=\frac{100}{5}=20$

Therefore, there are 20 terms in the given arithmetic progression.