Answers

2016-07-14T11:56:49+08:00
Given:
a1 = 3, an = 46,875, r = 5, n = ?, Sn = ?

Solving for n:
an = a1 ⚫r^(n - 1)
46,875 = 3 ⚫ 5^(n-1)
5^(n - 1) = 46,875 ÷ 3
5^(n - 1) = 15,625

In order to get the value of n, you need to express 15,625 into base 5 so that it would have the same base as 5^(n - 1) so...

5^(n - 1) = 5^6

Both terms finally had the same base! Since the base are equal, then the exponents are also equal so...

n - 1 = 6
n = 6 + 1
n = 7

SOLVING FOR Sn (Sum of the terms:

sn = [a1 (1 - r^n)] ÷ (1 - r)
sn = [3 (1 - 5^7)] ÷ (1 - 5)
sn = [3 (1 - 78, 125)] ÷ (-4)
sn = (3⚫-78,124) ÷ (-4)
sn = -234,372 ÷ (-4)
sn = 58, 593

The sum of the terms of the geometric sequence is 58, 593 :)
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