Let the 5th, 7th, and 13th terms of the AP be T5,T7, and T13 respectively. ⇒T5=a+4d ⇒T7=a+6d ⇒T13=a+12d Since the terms are in GP: ⇒T72=T5×T13 ⇒(a+6d)2=(a+4d)×(a+12d) Expanding both sides: ⇒(a+6d)2=a2+12ad+48d2 ⇒a2+12ad+36d2=a2+12ad+48d2 Cancel out common terms: ⇒36d2=48d2 ⇒−12d2=0 Dividing through by d2 (assuming d≠0 ): ⇒a=−3d