Question

Given the formula, find the first five terms and the 10th term of each

sequence.
a n = -4 × 2 n-1
Can you teach me this?
Then I will try the next?

Answer 1

`\sf a_1=-4\\a_2=-12\\a_3=-20\\a_4=-28\\a_5=-36\\a_(10)=-76`

Explanation:

`\textsf{Given sequence}: \sf a_n=-4(2n-1)`

This formula is for the nth term of the sequence.

Therefore, to find any term of the sequence, substitute the position of the term you wish to find as n.

For example, to find the 10th term, substitute n = 10 into the formula:

`\begin{aligned}\sf a_(10) & =-4[2(10)-1)]\\ & = -4(20-1)\\ & = -4(19)\\ & = -76\end{aligned}`

To find the first 5 terms, substitute n = 1 through n = 5 into the formula:

`\sf a_1=-4[2(1)-1]=-4(2-1)=-4(1)=-4`

`\sf a_2=-4[2(2)-1]=-4(4-1)=-4(3)=-12`

`\sf a_3=-4[2(3)-1]=-4(6-1)=-4(5)=-20`

`\sf a_4=-4[2(4)-1]=-4(8-1)=-4(7)=-28`

`\sf a_5=-4[2(5)-1]=-4(10-1)=-4(9)=-36`

Answer 2

Given formula:
`\sf A_n= -4(2)^(n-1)`

simplify substitute the number of term by replacing n

Find first five terms:

`\sf A_1= -4(2)^(1-1)` ⇒
`\sf A_1= -4`

`\sf A_2= -4(2)^(2-1)` ⇒
`\sf A_2= -8`

`\sf A_3= -4(2)^(3-1)` ⇒
`\sf A_3= -16`

`\sf A_4= -4(2)^(4-1)`⇒
`\sf A_4= -32`

`\sf A_5= -4(2)^(5-1)`⇒
`\sf A_5= -64`

Tenth term:

`\sf A_(10)= -4(2)^(10-1)` ⇒
`\sf A_(10)= -2048`