Question

The fifth term of an arithmetic sequence is 22 and the 15th term is 62. Find the 100th term and the sum of the first 60 terms. I'm having trouble figuring out how to do this.

Answer 1

T15-T5 = 10d = 40
so, d = 4
Now you can find T1 and T60

Then the sum is 30(T1+T60)

Answer 2

First you use the known to find the unknown....
U2=22, n=5
U15=62, n=15
You use from the formular
Un=a+(n-1)d
from the fith term
22=a+(5-1)d
22=a+4d--------equation 1
From the 15th term
62=a+(n-1)d
62=a+(15-1)d
22=a+14d-------equation 2

a+4d=22 you subtract
a+14d=62
-10d=-40
d=4
Substitute the value or d in equa 1
a+4d=22
a+4×4=22
a+16=22
a=22-16
a=6
Now use the formular to find the 100th term
Un=a+(n-1)d
Good luck