In a geometric series, the first and fourth terms are 2048 and 256 respectively. Calculate r, the common ratio of the terms. The sum of the first n terms is 4092. Calculate the value of n.

A geometric series S always follows the same pattern: S = a + ar + ar^2 + ar^3 ... Here i've labelled the first term a, and the common ratio r. The next term in a geometric series is always the preceding term multiplied by r. So, we can assign values to a and ar^3 given we have been provided with the first and fourth terms. Now to find r. 256/2048 is the same as ar^3/a. The a's cancel out, which tells us r^3 is 1/8 and so r is 1/2. You need to know a formula to answer the next part. The sum for n terms in a geometric series is S = a(1-r^n)/(1-r). We know values for a, r and S, and we wish to determine a value for n. Solving this equation leads to n = 10.

SW
Answered by Sam W. Maths tutor

5937 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

Find the area bounded by the curve y=(sin(x))^2 and the x-axis, between the points x=0 and x=pi/2


Explain the chain rule of differentiation


A ball is released on a smooth ramp at a distance of 5 metres from the ground. Calculate its speed when it reaches the bottom of the ramp.


When is an arrangement a combination, and when a permutation?


We're here to help

contact us iconContact ustelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

MyTutor is part of the IXL family of brands:

© 2025 by IXL Learning