GP

The second term of a geometric progression is 3 and the fourth term is 12.
Find the first term, a
and the sum of the first 10terms,

Question say GP i.e. a, ar, ar^2, ar^3

• 2nd term ar = 3
• 4th term ar^3 = 12
• now divide ar^3 by ar and you get r^2 = 12/3 = 4
• r^2 = 4 then r=2
• Now ar = 3 so a(2) = 3 then a = 3/2

Sum of first 10 terms = a(1 - r^n)/(1 - r)

a = 3/2, r = 2 and n = 10 so substitute and solve