Question

find the common difference of an AP whose first term is 5 and sum of its first four term is half the sun of next four terms​

Answer 1

a = 5

The sum of first 4 terms, S1= 5 + (5 + d )+ (5 + 2d) + (5 + 3d) = 20 + 6d

Sum of next 4 terms, S2 = ( 5 + 4d) + ( 5 + 5d ) + ( 5 + 6d ) + ( 5 + 7d ) = 20 + 22d

2 × S1 = S2

2 ×( 20 + 6d ) = ( 20 + 22d )

20 + 6d = 10 + 11d

5d = 10

d = 2

Answer 2

$\huge\bf\green{\underline{\underline{Answer :}}}$

Let d be the common difference of given A.P.

First term (a)=5

$\huge\bf\green{\underline{\underline{Given :- }}}$

a1 +a2 +a3 +a4 = $\frac{1}{2}× (a5 +a6 +a7 +a8)$

⇒a+(a+d)+(a+2d)+(a+3d) = $\frac{1}{2} [(a+4d)+(a+5d)+(a+6d)+(a+7d)]$

⇒4a+6d = $\frac{1}{2} (4a+22d)$

⇒4a+6d = 2a+11d

⇒11d−6d = 4a−2a

⇒d = $\large\frac{2×5}{5}$

⇒d = 2

$\bf{Hence\: the\:common\: difference\:of\:}$

$\bf{given\: A.P. \:is \:2.}$

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