Question

Find the 7th term of the arithmetic sequence given a12=29 and
a16=53
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Answer 1

a7=-1

Explanation:

Arithmetic Sequences

The arithmetic sequences can be identified because each term n is obtained by adding or subtracting a fixed number to the previous term n-1.

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

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

We know: a12=29, a16=53, now we use the above equation for n=12 and n=16:

`a_1+(12-1)r=29`

`a_1+(16-1)r=53`

Simplifying both equations:

`a_1+11r=29`

`a_1+15r=53`

Subtracting:

`4r=53-29=24`

Solving:

r=24/4

r=6

The 7th term can be found as 9 terms before the 16th:

`a_7=a_(16)-9r`

`a_7=53-9*6=53-54=-1`

Thus: a7=-1