Question

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

Answer 1

Given,
a1 = 5 (first term)
sum of first 4 terms = sum of 1/2 of next four terms
i.e a1+a2+a3+a4 = 1/2(a5+a6+a7+a8)
we know that an = a+(n-1)d

a+(a+d)+(a+2d)+(a+3d) = 1/2(a+4d)+(a+5d)+(a+6d)+(a+7d)
where "d" is the common diff...

Substituting 5 in places of "a" we get,
5+(5+d)+(5+2d)+(5+3d)= 1/2(5+4d)+(5+5d)+(5+6d)+(5+7d)
20+6d = 1/2(20+22d)
20+6d = 10+11d
5d=10
d=2








Hope it helps... :)

Answer 2

Answer:

d=2

Step-by-step explanation:

let d is common difference of AP

now first 4term is 5,5+d,5+2d,5+3d

and next 4term 5+4d,5+5d,5+6d,5+7d

now according to question  

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

20+6d=10+11d

d=2