Question

If 21, a, b, -3 are in AP then find the value of a and b

Answer 1

Given :-

A.P :- 21 , a , b , -3

=> As , we know the half of the sum of left and right A.P is equal to middle one

by this

we get,

=> (21 + b ) /2 = a

21 + b = 2a

2a - b -21 = 0 .......... ( i )




Now ,


=> ( a -3 ) / 2 = b

a - 3 = 2b

a - 2b -3 = 0 ........ ( ii ) × 2

sub ( ii ) ×2 from ( i )

2a - b - 21 - ( 2a - 4b -6 ) = 0

2a - b - 21 - 2a + 4b + 6 = 0

3b - 15 = 0

b = 15 /3

b = 5


putting value of b in equation ( i )

2a - b - 21 = 0

2a - 5 - 21 = 0

2a - 5 - 21 = 0

2a -26 = 0

a = 26/2

a = 13




So, a = 13
and b = 5



@Altaf