Question

if 18, a, b, -3 are in AP then a + b is equal to​

Answer 1

Step-by-step explanation:

if we take any three terms in an AP

the middle term is the arithmetic mean of the two

applying this

(18+b)/2=a......1

(a-3)/2=b.......2

by eq 1

18+b=2a

b=2a-18......3

substituting 3 in eq2

a-3=2(2a-18)

a-3=4a-36

3a=33

a=11......4

substituting 4 in 3

b=22-18

b=4

therefore a+b=15

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SHORTCUT

18=A (first term of AP)

-3=A+3D where D is common difference

add. 15=2A+3D......1

and a=A+D. b=A+2D

a+b=2A+3D.....2

by eq 1 and 2

a+b=15..