Question

If the sum of three terms in $A.P.$ is $-3$ and their product is $8$, then sum of their square

• A. $21$
• B. $10$
• C. $12$
• D. $9$

Answer 1

The correct option is A $21$

Let the three numbers in A.P. be $a-d,a,a+d$.

By the problem

$(a-d)+a+(a+c)=-3$

or, $3a=-3$

or, $a=-1$........(1).

Again given $(a-d).a.(a+d)=8$

or, $a.(a^2-d^2)=8$

or, $1-d^2=-8$ [Using value of $a$]

or, $d^2=9$......(2).

Now $(a-d{)}^2+a^2+(a+d{)}^2$

$=2(a^2+d^2)+a^2$

$=2(1+9)+1$ [Using (1) and (2)]

$=21$.