Question

Find the first 5 terms given the nth term.


`\\ \qquad \qquad \large \boxed{ \bf{ \: \: a_n = (- 2)^n \: \: }}`

`\\`

`\qquad \sf \red{Need \: the \: exact \: and \: correct} \: \\ \sf \qquad \red{ answer \: and \: solution}.`
​

Answer 1

-2, 4, -8, 16, -32, ...

Explanation:

To find any term given the nth term, simply substitute the value of n into the given nth term equation.

Given nth term equation:

`\large \boxed{\rm a_n=(-2)^n}`

Therefore, to find the first 5 terms, substitute the values of n of 1 through 5 into the nth term equation, remembering to apply the following exponent rules:

`\rm (-a)^n=-a^n, \quad \textsf{if }n \textsf{ is odd}`

`\rm (-a)^n=a^n, \quad \textsf{if }n \textsf{ is even}`

First 5 terms

`\rm a_1=(-2)^1=-2`

`\rm a_2=(-2)^2=4`

`\rm a_3=(-2)^3=-8`

`\rm a_4=(-2)^4=16`

`\rm a_5=(-2)^5=-32`

Answer 2

• -2,4,-8,16,-32

Explanation:

let's understanding the question situation,

we have to find the first 5 terms given the nth term.

According to the question,

The given term is

`\\ \qquad \qquad \large \boxed{ \sf{ \: \: a_n = (- 2)^n \: \: }}`

Solution:-

• 
  `{ \sf{ \: \: a_(1) = (- 2)^(1)=\bold{-2} \: \: }}`

• 
  `{ \sf{ \: \: a_(2) = (- 2)^(2)=\bold{4} \: \: }}`

• 
  `{ \sf{ \: \: a_(3) = (- 2)^(3)=\bold{-8} \: \: }}`

• 
  `{ \sf{ \: \: a_(4) = (- 2)^(4)=\bold{16} \: \: }}`

• 
  `{ \sf{ \: \: a_(5) = (- 2)^(5)=\bold{-32} \: \: }}`

Final answer:-

.°. The First 5term is -2,4,-8,16,-32.