Question

the sum of the first 20 terms of an A.P is identical to the sum of the first 22 term.If the common difference is -2; find the first terms​

Answer 1

First term a = 41

Explanation:

Arithmetic Progression:

Common differences d = -2

`S_(n)=(n)/(2)(2a+[n-1]d)\\\\S_(20)=(20)/(2)(2a+19*[-2])\\\\`

= 10*(2a - 38)

= 10*2a - 10*38

=20a - 380

`S_(22)=(22)/(2)(2a+21*[-2])\\\\`

= 11 (2a -42)

=11*2a - 11*42

= 22a - 462

`S_(22)=S_(20)\\\\`

22a - 462 = 20a - 380

22a = 20a - 380 + 462

22a = 20a + 82

22a - 20a = 82

2a = 82

a = 82/2

a = 41

First term a = 41