if x+2 ,2x, x+3 are three consecutive terms of AP then find x
can I get fast and correct ans please
Answers
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
- a= x+2
- b = 2x
- c = 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