Question

Q1.The value of x, for which 2x, x+ 10, 3x + 2 are three consecutive terms of an AP
i) 6
ii) -6
iii) 18
iv) -18​

Answer 1

Explanation:

Given

2x, x+10 and 3x+2 are three consecutive terms of an ap

To Find

we have to find the value of x

Since, all three terms are consecutive terms so,their common difference must be equal to each other.

First term = 2x

second term = x+10

third term = 3x+2

Now, finding the common difference

D =2nd term - 1st term

D1= x+10-2x

Now,

D2= 3rd term -2nd term

D2= 3x+2-(x+10)

Now, comparing both common difference

=> D1= D2

=> x+10-2x= 3x+2-x-10

=> -x+10= 2x-8

=>-3x= -8-10

=> -3x= -18

=> x= 6

Check:

Now, finding the terms

1st term = 2*6= 12

2nd term= 6+10= 16

3rd term= 3*6+2= 18+2= 20

D1= 16-12=4

D2= 20-16= 4

Since,D1= D2