The sum of the first 7 terms of a geometric sequence is 16383. The common ratio is 4. What is the fourth term of the sequence? The fourth term is (A)12 (B)48 (C)152 D.769
Mathematics · Middle School · Wed Jan 13 2021
llm
Answered on
Formula used :
Sn=a(r^n −1)/(r-1)
We have,
r = 4
S7 = 16383
a4 = ?
So,
S7 = a.4^7 -1/(4-1)
16383 = a. 16384 - 1/ 3
a = 16383 × 3/ 16383
a = 3
Now,
a4 = ar^n -1
a4 = 3.4^4-1
= 3.(4^3)
= 3.(64)
= 192
Hence, fourth term of sequence is 192.