Write an expression for the apparent nth term of the sequenc

Write an expression for the apparent nth term of the sequence. (Assume n begins with 1.) 1/2, -1/4, 1/8 -1/16, .............

Solution

This is a geometric progression with first term(a) =1/2 and common ratio(r) = -1/2.

the n^th term of a geometric sequence is given by, t_n = ar^n-1

For eg- 10^th term will be t₁₀ = (1/2)(-1/2)⁹ = -(1/512)...............

Sum till infinity = a/(1-r) = (1/2)/(1/2) = 1.....................