The sum of the first 15 terms of an arithmetic series is 1290. The sum of the first 16 terms is 1464. Find t16. Find S20

Answer 1

sum(15) = (15/2)(2a + 14d) = 1290
2a + 14d =172

sum(16) = (16/2)(2a + 15d) = 1464
2a + 15d = 183
subtract them:
d = 11
sub into 2a + 14d = 172
2a + 154 = 172
2a = 18
a = 9

term(16) = a + 15d = 174

sum(20) = 10(2a + 19d) = 10(18+209) = 2270

BTW, we could have found term (16)
by Sum(16) - sum(15) = 1464-1290 = 174

but we needed both a and d to find sum(20)