The correct option is A 8 and ±5
Let the given terms be (a−d),a and (a+d), where d is common difference.
Given sum of terms = 24
∴(a−d)+a+(a+d)=24
⇒3a=24⟹a=8
So the terms are (8−d),8 and (8+d).
Given product of terms = 312.
∴(8−d)×8×(8+d)=312
⇒(8−d)(8+d)×8=312
⇒82−d2=3128=39
⇒64−d2=39
⇒d2=25
⇒d=±5
So, the middle term of the AP is 8 and common difference is ±5.