Question

the 2nd and 5th term of gp are-1\2 and1\16SO FIND THE SUM Of gp up to 8th term

Answer 1

It's 54.

The nth tern of a Geometric Progression is obtained as  

T(n) = a * r ^ (n-1)  

where a is the first term of the GP and r is T(n+1)/T(n)

So we know that  

T(1) = 16 = a * r^(1-1) and

T(5) = 81 = a * r ^ (5-1)

Dividing the two terms, we get

81 / 16 = (a * r^4) / (a)

r^4 = 81/16 implies r = 3/2.

Using the nth term formula, we get

T(4) = 16 * (3/2) ^ 3 = 54.

Answer 2

a.r=-1/12  a.r^4=1/16  ⇒ a=1 and r=-1/2 which is less than one.

S=a(1-r^n)/(1-r)=1(1-1/2^8)/(1-(-1/2)) =((256-1)/256)/(3/2) =85/128