Question

The sum of first $3$ elements of $A.P$ is $\frac{13}{12}$ & their product is $-1$. Find the common difference in the elements.

Answer 1

Let $(a-d),a$ and $(a+d)$ be nthe three elements in A.P.

Sum of elements $=\frac{13}{12}$

$(a-d)+a+(a+d)=\frac{13}{12}$

$\Rightarrow a=\frac{13}{36}$

Product of elements $=-1$

$(a-d)\left(a\right)(a+d)=-1$

$\Rightarrow a^2-d^2=-1-\frac{13}{36}$

$\Rightarrow d^2=\frac{169}{1296}+\frac{49}{36}$

$\Rightarrow d=\sqrt{\frac{169+1764}{1296}}=\frac{\sqrt{1933}}{36}$