Question

Write the first five terms of the sequence defined by ${\displaystyle a_n={(–1)}^{n-1}.2^n}$

Answer 1

${\displaystyle a_n={(–1)}^{n-1}\times 2^n}$

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

${\displaystyle a_1={(–1)}^{1-1}\times 2^1={(–1)}^0\times 2=2}$

${\displaystyle a_2={(–1)}^{2-1}\times 2^2={(–1)}^1\times 4=–4}$

${\displaystyle a_3={(–1)}^{3-1}\times 2^3={(–1)}^2\times 8\times 8}$

${\displaystyle a_4={(–1)}^{4-1}\times 2^4={(–1)}^3\times 16=–16}$

${\displaystyle a_5={(–1)}^{5-1}\times 2^5={(–1)}^4\times 32=32}$

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