Question

t3=t7=6 t3*t7=8 find a and d of an ap

Answer 1

Answer :

t3= a+2d

t7= a+6d

t3+ t7 = 6

⇒a+2d+a+6d = 6

⇒2a+ 8d =6

⇒a = 6-8d / 2

⇒a= 3- 4d ---------------(i)

Now,

(a+2d)(a+ 6d) = 8

⇒a² +6da +2da +12d²=8

apply (i),

(3-4d)² + 8d (3-4d)+ 12 d²=8

⇒9+16d²_24d+24d-32d²+12d²=8

⇒-4d² +9 =8

⇒-4d²= -1

⇒d²= 1/4

⇒d=1/2 ---------------(ii)

Apply (ii) in (i):-

a= 3-4d

⇒a=3- 4× 1/2

⇒a =1

Step-by-step explanation:

@Genius