Question

Find an equation for the nth term of the arithmetic sequence.
-15, -6, 3, 12, ...

Answer 1

aₙ = 9n - 24 is the nth term of arithmetic sequence.

Explanation:

we have given arithmetic sequence:

-15, -6, 3, 12, ...

we have to find the nth term of the arithmetic sequence.

consider the given arithmetic sequence -15, -6, 3, 12, ...

here a₁= -15 , a₂= -6 ,a₃ = 3,......

we first find the common difference between consecutive terms (d).

common difference can be find by finding difference between two successive terms of give arithmetic sequence -15, -6, 3, 12, ...

a₂ - a₁ =( - 6 ) - ( - 15) = 9

a₃ - a₂ = ( 3 ) - ( - 6 ) = 9

hence common difference of given arithmetic sequence is 9.

thus the formula to find the nth term of arithmetic sequence is given below

aₙ = a +( n - 1 ) d

putting a = -15 , d = 9 we get

aₙ = ( -15 ) + ( n-1 ) 9

aₙ = - 15 + 9n - 9

aₙ = 9n - 24 this is the nth term of arithmetic sequence.

Answer 2

The nth term of AP is calculated as
`a_n=9n-24`

Explanation:

Given : An arithmetic sequence -15, -6, 3, 12, ...

We have to find the nth term of the given arithmetic sequence -15, -6, 3, 12,..

Consider the given arithmetic sequence -15, -6, 3, 12, ...

Here,
`a_1=-15\ ,a_2=-6\ ,a_3=3`

We first find the common difference (d)

Common difference can be find by finding difference between two successive terms of given arithmetic sequence.

`a_2-a_1=-6+15=9\\\\ a_3-a_2=3+6=9`

Thus, common difference of given AP is 9

Thus, The equation to find the nth term of AP is calculated as,

`a_n=a+(n-1)d`

Substitute a = -15 , d = 9 , we get,

`a_n=-15+(n-1)9\\\\ a_n=-15+9n-9\\\\ a_n=9n-24`

Thus, the nth term of AP is calculated as
`a_n=9n-24`