Question

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

• A. 15 or -9
• B. -15 or 9
• C. -15 or -9
• D. 15 or 9

Answer 1

The correct option is B

-15 or 9

Let the first term of Arithmetic sequence be 'x' Then second term is x+6 $(\because$ common difference is 6)

$\Rightarrow \left(x\right)(x+6)=135$ (Given)

$\Rightarrow x^2+6x-135=0$

$\Rightarrow x^2+15-9x-135=0$

$\Rightarrow x(x+15)-9(x+15)=0$

$\Rightarrow (x+15)(x-9)=0$

$\Rightarrow x=-15$ or x=9

Verification: If the first term is 9 then second term will be 9+6=15

Their product -(9)(15)=135

If the first term is -15 then second term will be -15+6=-9

Their product is (-9)(-15)=135