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Formula for Sum of n Terms of an AP

The sum of fi...

Question

The sum of first n terms of an A.P. whose first term is 8 and the common difference is 20 is equal to the sum of first 2n terms of another A.P whose first term is -30 and common difference is 8. Find the value of n.

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Solution

The correct option is D 11
Given
$a_{1}$ = 8 $a_{2}$ = -30
$d_{1}$ = 20 $d_{2}$ = 8

$S_{n} = S_{2 n}$

$\frac{n}{2} (2 a_{1} + (n - 1) d_{1}) = \frac{2 n}{2} (2 a_{2} + (2 n - 1) d_{2})$

$\Rightarrow$ 16+(n-1)20 = 2 [ -60 + (2n-1) 8]

$\Rightarrow$ 16 + 20n -20 = -120 + 32n -16

$\Rightarrow$ 12n = 132

$\Rightarrow$ n = 11

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The sum of first n terms of an A.P. whose first term is 8 and the common difference is 20 is equal to the sum of first 2n terms of another A.P whose first term is -30 and common difference is 8. Find the value of n.

The correct option is D 11Given a1 = 8 a2 = -30 d1 = 20 d2 = 8 Sn=S2n n2(2a1+(n−1)d1)=2n2(2a2+(2n−1)d2) ⇒16+(n-1)20 = 2 [ -60 + (2n-1) 8] ⇒16 + 20n -20 = -120 + 32n -16 ⇒ 12n = 132 ⇒ n = 11