Question

How many terms are there in the A.P.?
$7,10,13,........,43$

Answer 1

Given sequence is $7,10,13,...,43$

The first term $a=7$ and

the common difference $d=10-7=3$

the last term is $43$

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, $a+(n-1)d=43$

$⟹7+(n-1)\ast \left(3\right)=43$

$⟹7-3+3n=43$

$⟹4+3n=43$

$⟹3n=43-4$

$⟹n=\frac{39}{3}$

$⟹n=13$

Therefore, the number of terms in the given sequence is $13$