The seconds term of a geometric series is 4 while the fourth term is 16. Find the sum of the first five terms

Assessment: JAMB UTME - Mathematics - 2011 Subject: General Mathematics

Question 1 Report

The seconds term of a geometric series is 4 while the fourth term is 16. Find the sum of the first five terms
Answer Details
T2 = 4, T4 = 16
Tx = arn-1
T2 = ar2-1 = 4 i.e. ar3 = 16, i.e. ar = 4
T4 = ar4-1
therefore,  T 4 T r  =  a r 3 a r  =  16 4
r2 = 4 and r = 2
but ar = 4
a =  4 r  =  4 2
a = 2
Sn =  a ( r n − 1 ) r − 1
S5 =  2 ( 2 5 − 1 ) 2 − 1
=  2 ( 32 − 1 ) 2 − 1
= 2(31)
= 62

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