Question

find the common difference of an AP whose first term is 5 and the sum of its first 4 terms is half the sum of the next four terms. please give this answer fast. its urgent.

Answer 1

Answer:

Step-by-step explanation:

the formula for nth term in an AP is given by

a+(n-1)d

so given first term is 5 so second term will be 5+d and third term will be 5+2d

here two is the common difference

so the sum of first four terms will be 5+5+d+5+2d+5+3d=

20+6d

the sum of next four terms is given by 5+4d+5+5d+5+6d+5+7d=

20+22d

so the sum of the first four terms if half the sum of the next four terms

(20+6d)=20+22d/2

2(20+6d)=20+22d

40+12d=20+22d

by solving the above equation

we get 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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