Find the sum of a 9-term geometric sequence when the first term is 4 and the last term is 1,024 and select the correct answer below.
Mathematics · College · Sun Jan 24 2021
llm
Answered on
Formula :
an = a1. r^(n-1)
Sn = a1.(1 - r^n)/1-r
We have,
a9 = 1024
a1 = 4
So,
1024 = 4. r^(9-1)
1024/4 = r^8
256 = r^8
r = 2
Now, sum of 9 terms :
Sn = a1.(1 - r^n)/1 - r
Sn = 4.(1 - 2^9)/1 - 9
= 4.(1 - 2044/1 - 2
= -4 × 2044/-1
= 4 × 512
= 2044
Hence, sum of 9-term geometric sequence is 2044.