Sum

Write the first five terms of the sequence defined by `a_n = (–1)^(n-1) . 2^n`

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#### Solution

`a_n = (–1)^(n-1) × 2^n`

Putting n = 1, 2, 3, 4, and 5 we get

`a_1 = (–1)^(1-1) × 2^1 = (–1)^0 × 2 = 2`

`a_2 = (–1)^(2-1) × 2^2 = (–1)^1 × 4 = – 4`

`a_3 = (–1)^(3-1) × 2^3 = (–1)^2 × 8 × 8`

`a_4 = (–1)^(4-1) × 2^4 = (–1)^3 × 16 = –16`

`a_5 = (–1)^(5-1) × 2^5 = (–1)^4 × 32 = 32`

Thus the first five term of the sequence are 2, –4, 8, –16, 32.

Concept: Arithmetic Progression

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