+0  
 
+4
617
1
avatar

How many terms are there in a geometric series if the first term is 5, the common ratio is 2, and the sum of the series is 315?

Hint:  r ≠ 1, where a1 is the first term and r is the common ratio.

 n = 3 n = 4 n = 5 n = 6

Guest Mar 13, 2017
 #1
avatar
+5

Sum =F x [1 - R^N] / [1 - R]

315 = 5 x [1 - 2^N] / [1 - 2]

 

Solve for N over the real numbers:
315 = 5 (2^N - 1)

315 = 5 (2^N - 1) is equivalent to 5 (2^N - 1) = 315:
5 (2^N - 1) = 315

Divide both sides by 5:
2^N - 1 = 63

Add 1 to both sides:
2^N = 64

64 = 2^6:
2^N = 2^6

Equate exponents of 2 on both sides:
Answer: |N = 6

Guest Mar 13, 2017

9 Online Users

New Privacy Policy

We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive information about your use of our website.
For more information: our cookie policy and privacy policy.