Question

please answer for this question ​

Answer 1

Step-by-step explanation:

A(3) + A(7) = 6

a + 2d + a + 6d = 6

2a + 8d = 6

a + 4d = 3 ------(1)

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

a² + 6ad + 2ad + 12d² = 8

a² + 8ad + 12d² = 8

(a + 4d)² - 4d² = 8

(3)² - 4d² = 8

9 - 8 = 4d²

4d² = 1

d² = 1/4

d = 1/2

then , a = 3 - 4(1/2)

a = 3 - 2 = 1

15th term = A(15)

= a + 14d

= 1 + 14(1/2)

= 1 + 7

= 8

Answer 2

Step-by-step explanation:

a+2d + a+6d= 6

a+4d=3

a=3-4d........(1)

now product

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

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

a^2+8ad +12d^2=8....(2)

now put value of a in eq 2

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

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

-4d^2+9=8

-4d^2 = -1

-d^2=-1/4

d= 1/2

putting value of d in eq 1

a+4d=3

a+2 = 3

a= 1

3rd term = 2

6th term = 4

15th term of ap

a + 14d=

1+7=8