Question

The first and the last terms of an AP are 8 and 350 respectively. If its common difference is 9, how many terms are there and what is their sum?

Answer 1

Formula of n= a+(n-1)d

350=8+(n-1)9

350=8+9n-9

9n=351

n=39

now sum=n/2(a+l)

39/2(8+350)

39/2×358=39×179=6981

Thank

Answer 2

Answer:

$n = 39 ,\\S_{39}=6981$

Step-by-step explanation:

$Given\\first \:term (a)=8,\\last\:term (l)=350,\\common\: difference (d)=9\:in \: A.P$

$Let \: number \: of \: terms \: in \: A.P = n$

$a+(n-1)d=l$

$\implies 8+(n-1)9=350$

$\implies (n-1)9=350-8$

$\implies (n-1)9=342$

$\implies n-1=\frac{342}{9}$

$\implies n = 38+1$

$\implies n = 39$

$Now,\\Sum \: of \: n \: terms (S_{n})= \frac{n}{2}(a+l)$

$\implies S_{39}=\frac{39}{2}(8+350)\\=\frac{39}{2}\times 358\\=39\times 179\\=6981$

Therefore,

$n = 39, \\S_{39}=6981$

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