If the 2nd term of a gp is 6 and the 4th term is 54 find the sum of the first 5 term
Nope, the robot tutor messes up another simple math problem
correct solution:
ar = 6 and ar^3= 54
therefore r^2 = 9 ----> r = ± 3
if r = 3, a = 2
and sum(5) = 2( 3^5 - 1)/(3-1) = 242
if r = -3, a = -2
and sum(5) = -2( (-3)^5 - 1)/(-3-1)
= -2(-244)/-4 = -122
OR, we can just find the sum of 5 terms:
case1: 2 + 6 + 18 + 54 + 162 = 242
case 2: -2 + 6 - 18 + 54 - 162 = -122
The sum of the first 5 terms of a GP is given by S5 = a1(1 - r5)/(1 - r), where a1 is the first term, r is the common ratio and r5 is the fifth term.
In this case, a1 = 2, r = 3 and r5 = 243.
Therefore, S5 = 2(1 - 243)/(1 - 3) = -240.