Let there be an A.P with first term $a$ , common difference $d$ . If $a_{n}$ denotes its $n$ th term and $S_{n}$ the sum of first $n$ terms, find
$d$ , if $a = 3, n = 8$ and $S_{n} = 192$

d = 6

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d = 8

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d = 5

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d = 9

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Solution

The correct option is A $d = 6$
$a = 3, n = 8, S_{n} = 192$

$S_{8} = 192$

$\frac{8}{2} [6 + 7 d] = 192$

$6 + 7 d = 48$

$7 d = 42$
$d = 6$

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Similar questions

Q. Let there be an A.P. with first term 'a', common difference 'd'. If a_n denotes in n^th term and S_n the sum of first n terms, find.

(i) n and S_n, if a = 5, d = 3 and a_n = 50.

(ii) n and a, if a_n = 4, d = 2 and S_n= −14.

(iii) d, if a = 3, n = 8 and S_n = 192.

(iv) a, if a_n = 28, S_n = 144 and n= 9.

(v) n and d, if a = 8, a_n = 62 and S_n = 210

(vi) n and a_n, if a= 2, d = 8 and S_n = 90.

Q. Let there be an A.P with first term

a

, common difference

d

. If

a_{n}

denotes its

n

th term and

S_{n}

the sum of first

n

terms, , if

a_{n} = 4, d = 2

and

S_{n} = - 14

then

| n + a |

Let there be an A.P. with first term 'a', common difference 'd'. If $a_{n}$ denotes its nth term and $S_{n}$ the sum of first n terms, find.
(i) n and $S_{a}$ , if a=5, d=3 and $a_{n}$ =50.
(ii) n and a, if $a_{n}$ =4, d=2 and $S_{n}$ =-14.
(iii) d, if a=3, n=8 and $S_{n}$ =192.
(iv)a, if $a_{n}$ =28, $S_{n}$ =144 and n=9.
(v) n and d, if a=8, $a_{n}$ =62 and $S_{n}$ =210.
(vi) n and $a_{n}$ , if a = 2, d=8 and $S_{n}$ =90.
(vii) k, if $S_{n} = 3 n^{2}$ +5n and $a_{k}$ =164.
(viii) $S_{22}$ , if d =22 and $a_{22}$ =149

Let $S_{n}$ denote the sum of n terms of an A.P. whose first term is a. If the common difference d is given by $d = S_{n} - k S_{n - 1} + S_{n - 2}$ , then k =