if x+2 ,2x, x+3 are three consecutive terms of AP then find x

can I get fast and correct ans please

# if x+2 ,2x, x+3 are three consecutive terms of AP then find x

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[tex]{Solution}[/tex]

## Given :-

x +2 , 2x , x+3 are in A.P

## To find :-

Value of x

## SOLUTION:-

As they are in A.P Since, their terms difference should be same

If a, b , c are in A.P

## c – b = b – a So,

x + 2 , 2x , x+3

c – b = b- a

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

x+3 -2x = 2x -x -2

x-2x + 3 = x-2

-x + 3 = x-2

-x -x = -3 -2

-2x = -5

2x = 5

## x = 5/2

So, the value of x is 5/2

## Know more:-

A.P means Arthemetic progression That means it follows a certain pattern that is The given sequence common difference should be same

## Examples :-

2, 4 , 6 , 8 , 10. . . .

It is a Arthemetic progression beacuse its common difference is same i.e

10- 8 = 2

8 – 6 = 2

6 – 4 = 2

4 – 2 = 2

If you observe the difference that is 2 ,Since it is in A.P .

2, 4 , 6 , 8 , 10 .. . In this progression,

a = 2 [first term]

d = 2[common difference]

n = nth term

For finding nth term we have formula

an = a+(n-1) d

For finding sum of the terms we have formula that is

Sn = n/2 × 2a+(n-1)d