Question

The first and the last terms of an A.P are $17$ and $350$ respectively. If the common difference is $9$, how many terms are there and what is their sum?

Answer 1

Given

first term of A.P $a_1=17$

last term of A.P $a_n=350$

common difference $d=9$

the $n$th term of an A.P is given by

$a_n=a_1+(n-1)d$

for finding number of terms (n) put last term of A.P $a_n=350$ in above equation

$350=17+(n-1)9$

$17+9n-9=350$

$9n+8=350$

$n=\frac{350-8}{9}=\frac{342}{9}$

$n=38$

sum of n term of an A.P is given by .

$S_n=\frac{n}{2}(a_1+a_n)$

$⟹S_{38}=\frac{38}{2}(17+350)$

$⟹S_{38}=19\times 367$

$⟹S_{38}=6973$

hence number of terms in the A.P is n=38 and there sum is $S_{38}=6973$