Question

Arrange the below G.P in ascending order of the sum of there first three terms from top to bottom.

• A. 3,6,12,24,......
• B. 32,16,8,4,2,....
• C. 2,8,32,128,.....
• D. 1,3,9,27,81,....

Answer 1

Case(1):
3,,6,12,24,....
r = $\frac{6}{3}=2$
So, | r| >1
S3 = $\frac{a(r^3-1)}{r-1}=\frac{3(2^3-1)}{2-1}$
= 21
Case(2):
32,16,8,4,2,....
r = $\frac{16}{32}=\frac{1}{2}$
So, | r| <1
S3 = $\frac{a(1-r^3)}{1-r}=\frac{32(1-(\frac{1}{2}{)}^3)}{1-\frac{1}{2}}$
= 56

Case(2):
2,8,32,128,.....
r = $\frac{8}{2}=4$
So, | r| >1
S3 = $\frac{a(r^3-1)}{r-1}=\frac{2(4^3-1)}{4-1}$
= 42
Case(4):
1,3,9,27,81,....
r = $\frac{3}{1}=3$
So, | r| >1
S3 = $\frac{a(r^3-1)}{r-1}=\frac{1(3^3-1)}{3-1}$
= 13