Mathematics: 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

cStep-by-step explanation:588/2= 294...

the sum of the first 20 terms of an A.P is identical

jaylinzavala

30.01.2022

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

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