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:
[tex]a_n=a_1+(n-1)r[/tex]
We know: a12=29, a16=53, now we use the above equation for n=12 and n=16:
[tex]a_1+(12-1)r=29[/tex]
[tex]a_1+(16-1)r=53[/tex]
Simplifying both equations:
[tex]a_1+11r=29[/tex]
[tex]a_1+15r=53[/tex]
Subtracting:
[tex]4r=53-29=24[/tex]
Solving:
r=24/4
r=6
The 7th term can be found as 9 terms before the 16th:
[tex]a_7=a_{16}-9r[/tex]
[tex]a_7=53-9*6=53-54=-1[/tex]
Thus: a7=-1
