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

Answer:

First term a = 41

Step-by-step explanation:

Arithmetic Progression:

Common differences d = -2

$S_{n}=\frac{n}{2}(2a+[n-1]d)\\\\S_{20}=\frac{20}{2}(2a+19*[-2])$

  = 10*(2a - 38)

 = 10*2a - 10*38

=20a - 380

$S_{22}=\frac{22}{2}(2a+21*[-2])$

= 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