Question

Find the 61st term of -12, -28, -44,

Answer 1

`a_(61)=-972`

Explanation:

Arithmetic Sequences

The arithmetic sequences are identified because any term n is obtained by adding or subtracting a fixed number to the previous term. That number is called the common difference.

The equation to calculate the nth term of an arithmetic sequence is:

`a_n=a_1+(n-1)r`

Where

an = nth term

a1 = first term

r = common difference

n = number of the term

We are given the first terms of a sequence:

-12, -28, -44,...

Find the common difference by subtracting consecutive terms:

r = -28 - (-12) = -16

r = -44 - (-28) = -16

The first term is a1 = -12. Now we calculate the term n=61:

`a_(61)=-12+(61-1)(-16)`

`a_(61)=-12-60*16=-12-960`

`\mathbf{a_(61)=-972}`