Find whether 55 is a term of
Question:

Find whether 55 is a term of the AP 7, 10, 13, … or not. If yes, find which term it is.

Solution:

Yes, let the first term, common difference and the number of terms of an AP are a, d and n respectively.

Let the nth term of an AP be 55. i.e., Tn = 55.

Let the $n$th term of an AP be 55. i.e.. $T_{n}=55$.

We know that, the $n$th term of an AP, $T_{n}=a+(n-1) d$ …(i)

Given that, first term $(a)=7$ and common difference $(d)=10-7=3$

From Eq. (i), $\quad 55=7+(n-1) \times 3$

$\Rightarrow \quad 55=7+3 n-3 \Rightarrow 55=4+3 n$

$\Rightarrow \quad 3 n=51$

$\therefore \quad n=17$

Since, $n$ is a positive integer. So, 55 is a term of the AP. Now, put the values of $a, d$ and $n$ in Eq. (i),

$T_{n}=7+(17-1)(3)$

$=7+16 \times 3=7+48=55$

Hence, 17 th term of an AP is 55 .