Question

The sum of first 3 terrms of an A.P is 42 and the product of the first term and last term is 52.Find the first term and common difference.​

Answer 1

Let a-d , a, a+ d are in AP

ATQ,

(a-d)+a+(a+d)=42

3a= 42

a= 14

again

(a-d)(a+d)=52

$a^2-d^2$= 52

14²-d²=52

d²=196-52=144

d= ±12

hence, first term is (a - d) = 2 [ when d = 12 ] and 26 [ when d = -12 ]

so, first term, a = 2 when common difference, d = 12

first term, a = 26 when common difference , d = -12