Question

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

Answer 1

We have, $a_n=(-1{)}^{n-1}.2^n$

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

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

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

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

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

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

The first five terms are $2,-4,8,-16,32$