Question

(3x+2) (5x-3) and (4x+7) are the thre
consecutive terms of an A.P. then
value of x is
a) 1 6) 3 c) d) 7​

Answer 1

a (first term)= (3x+2)

an (last term) = (4x+7)

n (number of terms)= 3

d (common difference)= a2-a1 = (5x-3) - (3x+2) = 5x-3 - 3x-2 = (2x - 5)

Formula

an = a + (n-1)d

(4x+7) = (3x+2) + (3-1)(2x-5)

4x + 7 = 3x+2 + 4x - 10

4x+7 = 7x - 8

7+8 = 7x-4x

15 = 3x

x=5

or

a2 - a1 = a3 - a2

5x - 3 - (3x+2) = 4x + 7 - (5x-3)

5x-3 - 3x -2 = 4x + 7 - 5x + 3

2x - 5 = 10 - x

3x = 15

x = 5

Answer 2

Answer:

(3x+2) (5x-3) = 4x+7

regrouping the like term

3x+5x+2-3= 4x+7

8x-1=4x+7

8x-4x=-1+7

4x=6

x=6/4

3/2