SOLUTION: The seventh term of a geometric sequence is twice the fifth term and the sum of the first seven terms is 254. All the terms are positive. Find the first term
Algebra ->
Sequences-and-series
-> SOLUTION: The seventh term of a geometric sequence is twice the fifth term and the sum of the first seven terms is 254. All the terms are positive. Find the first term
Log On
Question 1083161: The seventh term of a geometric sequence is twice the fifth term and the sum of the first seven terms is 254. All the terms are positive. Find the first term Answer by ikleyn(52802) (Show Source):
Let "a" be the first term of the progression and "r" be the common ratio.
Then = and = .
Therefore, = = 2, and, hence, = .
Then the sum is
254 = =
= =
= =
= .
Hence, a = .
Answer. The first term is a = .
