Sum of the first n terms of a geometric sequence with a1 = 2 and r = -1/2 is S_n = (4/3)(1 - (-1/2)^n). Evaluate S_5.

Boost your skills in A Level Further Mathematics Core Pure. Study with flashcards and multiple choice questions, each question is followed by hints and explanations. Get prepared for your exam with confidence!

Multiple Choice

Sum of the first n terms of a geometric sequence with a1 = 2 and r = -1/2 is S_n = (4/3)(1 - (-1/2)^n). Evaluate S_5.

For a geometric sequence, the sum to n terms is S_n = a1(1 - r^n)/(1 - r). Here a1 = 2 and r = -1/2, and the given expression matches S_n = (4/3)(1 - (-1/2)^n). To find S_5, compute (-1/2)^5 = -1/32, so 1 - (-1/32) = 33/32. Then S_5 = (4/3) * (33/32) = 11/8. Quick check by adding the first five terms: 2, -1, 0.5, -0.25, 0.125 sums to 1.375, which is 11/8. The value is 11/8.

For a geometric sequence, the sum to n terms is S_n = a1(1 - r^n)/(1 - r). Here a1 = 2 and r = -1/2, and the given expression matches S_n = (4/3)(1 - (-1/2)^n). To find S_5, compute (-1/2)^5 = -1/32, so 1 - (-1/32) = 33/32. Then S_5 = (4/3) * (33/32) = 11/8. Quick check by adding the first five terms: 2, -1, 0.5, -0.25, 0.125 sums to 1.375, which is 11/8. The value is 11/8.

More practice questions