Question

the product of first two terms of an arithmetic sequence with the common difference 6 is 135 find the first term

Answer 1

given d=6
t1 t2 are first 2 terms
product =135
a(a+d)=135
a(a+6)=135
a^2+6a-135=0
a^2+15a-9a-135=0
a(a+15)-9(a+15)=0
(a-9)(a+15)=0
a=9, -15
a=9 is considered
first term is a and answer is 9

Answer 2

let the two terms are
a, a+d
where common difference is d

given information,
d =6
a(a+d) = 135
put the value of d
a(a+6) = 135
a^2 + 6a = 135
a^2 + 6a -135 =0
a^2 + 15a - 9a -135 =0
a(a+15) - 9(a+15) =0
(a+15) (a-9) = 0
a= 9, -15