Question

The sum of the integers from 40 to 60, inclusive, is 1050. what is the sum of the integers from 60 to 80 inclusive?

Please help me find the pattern and how to use it instead of adding 60+61+62+63..... etc.

Answer 1

think of an arithmetic sequence where
a=60 and d=1. The sum of the 1st 21 terms is thus

21/2(2*60+20*1) = 1470

or, since each number is 20 more than the terms of the first sequence, add 21*20 = 400, to get 1470