Question

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

Answer 1

Answer:

a7=-1

Step-by-step 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