Question

The sum of the third and seventh term of an AP is 6 and their product is 8 . Find the first term and the commo difference,
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Answer 1

Answer:

a₃ + a₇ = 6

a+2d + a + 6d =6

2a + 8d=6

a + 4d = 3  

a=3-4d         ______eqn(1)

(a₃)(a₇)=8

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

a^2 + 6ad + 2ad + 12d^2= 8

a^2 + 12d^2 +8ad =8

putting eqn (1)

(3-4d)^2 + 12d^2 + 8(3-4d)(d)=8

9+16d^2- 24d + 12d^2 + 24d - 32d^2 =8

(9 - 8) + (16d^2 + 12d^2 - 32d^2) -24d +24d =0

1 - 4d^2 = 0

4d^2=1

d^2=1/4

d= 1/2

putting d= 1/2 in eqn (1)

a=3-4d

a= 3- 4(1/2)

a=3-2

a=1

so, first term of A.P. will be 1 and common difference will be 1/2.