Question

How many terms are there in the A.P., $7,13,19,...205$ ?

• A. $32$
• B. $33$
• C. $34$
• D. $35$

Answer 1

Answer: (C)

$34$

Given sequence is $7,13,19,...,205$

The first term $a=7$ and

the common difference $d=13-7=6$

the last term is $205$

Let the last term be the $n^{th}$ term

We know that the $n^{th}$ term of the arithmetic progression is given by $a+(n-1)d$

Therefore, $a+(n-1)d=205$

$⟹7+(n-1)\times \left(6\right)=205$

$⟹7-6+6n=205$

$⟹1+6n=205$

$⟹6n=205-1$

$⟹n=\frac{204}{6}$

$⟹n=34$

Therefore, the number of terms in the given sequence is $34$