Question

Find the 7th term of the arithmetic sequence given a12=29 and
a16=53
a7=___

Answer 1

Thus: a7=-1

Explanation:

Arithmetic Sequences

The arithmetic sequences are identified because each term is obtained by adding or subtracting a fixed number to the previous term.

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, thus

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

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

Simplifying:

`a_1+11r=29`

`a_1+15r=53`

Subtracting both equations:

`4r=53-29=24`

Solving:

`r=24/4`

r=6

The 7th term can be found as 5 terms before the 12nd:

`a_7=a_(12)-5r`

`a_7=29-5*6=29-30=-1`

Thus: a7=-1