The sum of the first 15 terms of the sequence an=10n+21

That is

the sum of all the terms from a1 to an when you are summing up n terms is n (a1+an) / 2

so

find the 1st and 15th term

1st term is a1=10 (1) = 21=10+21=31

15th term is a15=10 (15) + 21=150+21=171

and n=15

15 (31+171) / 2=15 (202) / 2=3030/2=1515

the sum of the first 15 term is 1515