Question

The first term of a geometric sequence is 3 and the fifth term is 768 what is the sum of the first 9 terms of the corresponding series

Answer 1

Answer:

262143

Step-by-step explanation:

$a_{n} = a r^{n - 1}$     a = 3   n = 5   $a_{5} = 768$

768 = 3(r)^4   where r is the common ratio

r^4 = 256

r = 4

S = $\frac{a(r^{n}-1) }{r - 1}$      n = 9    r = 4    a = 3

S = $\frac{3(4^{9}-1) }{4 - 1}$ = $\frac{3(262144-1) }{3}$

  = 262143