Question

Find four terms of AP whos esum is -4 and whose square is 84

Answer 1

Answer:

Let the four terms in AP are,

a-d, a, a+d, a+2d

According to first condition,

(a - d) + (a) + (a + d) + (a + 2d) = - 4

4a + 2d = - 4

2a + d = - 2

Squaring both sides, we get

4a^2 + 4ad + d^2 = 4 -------- (1)

According to second condition,

(a - d)^2 + (a)^2 + (a + d)^2 + (a + 2d)^2 = 84

a^2 - 2ad + d^2 + a^2 + a^2 + 2ad + d^2 + a^2 + 4ad + 4d^2 = 84

4a^2 + 4ad + 6d^2 = 84 ------------ (2)

Subtract equation (1) from equation (2)

4a^2 + 4ad + 6d^2 = 84

4a^2 + 4ad + d^2 = 4

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                5d^2 = 80

d^2 = 16  => d = +4 or -4 , a = - 7

Hence AP are a-d, a, a+d, a+2d

-13, -7, -3, 1 or -3, -7, -13, -15.

Step-by-step explanation: