Answer:
Thus: a7=-1
Step-by-step 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:
[tex]a_n=a_1+(n-1)r[/tex]
We know: a12=29, a16=53, thus
[tex]a_1+(12-1)r=29[/tex]
[tex]a_1+(16-1)r=53[/tex]
Simplifying:
[tex]a_1+11r=29[/tex]
[tex]a_1+15r=53[/tex]
Subtracting both equations:
[tex]4r=53-29=24[/tex]
Solving:
[tex]r=24/4[/tex]
r=6
The 7th term can be found as 5 terms before the 12nd:
[tex]a_7=a_{12}-5r[/tex]
[tex]a_7=29-5*6=29-30=-1[/tex]
Thus: a7=-1
