Question

Pls answer this question

Answer 1

x-2, 4x-1 and 5x+2 are in AP

⇒ (4x-1) - (x-2) = (5x+2) - (4x-1) [Difference between two consecutive terms is same.]

⇒ 4x -1 - x + 2 = 5x + 2 - 4x + 1

⇒ 3x + 1 = x + 3

⇒ 3x - x = 3 - 1

⇒ 2x = 2

⇒ x = 1

Hence, the value of x is 1

a = 4

d = 5

Tn = 109

Tn = a + (n-1)d

109 = 4 + (n-1)5

105 = 5n -5

5n = 110

n. = 22

Hence, 22nd term of the AP is 109.

Answer 2

Step-by-step explanation:

1. If they are in AP , let a1 = (x - 2) and a2 = (4x - 1) and a3 = (5x + 2)

So, a2 - a1 = d also, a3 - a2 = d

(4x - 1) - (x - 2) = (5x + 2) - (4x-1)

4x - 1 - x + 2 = 5x + 2 - 4x+1

3x + 1 = x + 3

3x - x = 3 - 1

2x = 2

x = 1