Question

Find sum of first ten terms of the G.P.3,-6, 12, -24,​

Answer 1

Answer:

First term= a=6 Common ratio = r = 1.2/6= 0.2 <1 n=10 Sum of n terms Sn= a(1- r^n)/(r-1) S10= [6*(1-(0.2)^10]/(1-0.2) = [6*(1-(0.2)^10]/(0.8)

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Answer 2

Answer:

Formula for finding sum of n terms,

Sn = [ a ( 1 - r ^n) ] / ( 1 - r) only if r is not equal to 1 and r is lesser than 1.

Sn = [ a ( r ^n - 1 ) ] / ( r - 1 ) only if r is not equal to 1 and r is greater than 1.

Where , a = 1st term in G. P

r = common ratio

n = number of terms.

Given that, a = 3

n = 10

Common ratio r = 2nd term / 1st term

= -6 / 3 = -2

r = - 2

Since r is - 2 which is less than 1. So we use the 1st formula.

Sn = [ a (1 - r^n ) ] / ( 1 - r )

S10 = [ 3 ( 1 - (-2)^10 ) ] / ( 1 - -2 )

= [ 3 ( 1 - (-2)^10 ) ] / 3

= [ 3 ( 1 - ( 2*2*2*2*2*2*2*2*2*2) ] / 3

= 3(1-1024)/3 = 1 - 1024 = - 1023

Sum of 1st ten terms of the given G.P is -1023