What is the sum of the first 10 terms of the geometric series 32 + 16 + 8 + ... ?

Here we need to use the formula for the sum of a geometric series up to n terms: s = a*(r^n-1)/(r-1). In this formula, 'a' is the first term of the series, 'r' is the common ratio between each consecutive term of the series, and 'n' is the number of terms in the series. We know n = 10, and can see that a = 32. r = 0.5, as each term in the series is half that of the previous term. We input these values into our formula to get: s = 32*(0.5^10-1)/(0.5-1). Inputting this into a calculator, we get the answer s = 63.9 (3 s.f.).

EC
Answered by Eleanor C. Maths tutor

11833 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

Simplify fully: (5 +√7)/ (2+√7)


Find the equation to the tangent to the curve x=cos(2y+pi) at (0, pi/4)


A curve has equation y = 20x -x^(2) - 2x^(3). The curve has a stationary point at the point M where x = −2. Find the x coordinates of the other stationary point.


A sweet is modelled as a sphere of radius 10mm and is sucked. After five minutes, the radius has decreased to 7mm. The rate of decrease of the radius is inversely proportional to the square of the radius. How long does it take for the sweet to dissolve?


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:

© 2026 by IXL Learning