Question

If the sum of three consecutive of an A.P. is $-3$ and their product is $8$, then which of the following is/are correct?

• A. The commmon difference can be $3$
• B. One of the term is $-1$
• C. Sum of the squares of the number is $21$.
• D. Sum of the squares of the number is $25$.

Answer 1

Answer: (A), (B), (C)

The correct options are
A The commmon difference can be $3$
B One of the term is $-1$
C Sum of the squares of the number is $21$.

Let the numbers be
$(a-d),a,(a+d)$
Now,
$(a-d)+a+(a+d)=-3\Rightarrow a=-1$
Also,
$(a-d)a(a+d)=8\Rightarrow a(a^2-d^2)=8\Rightarrow -1(1-d^2)=8\Rightarrow d=\pm 3$

Therefore, the number are $-4,-1,2$ or $2,-1,-4$
Sum of square $=21$