Question

if x-1,x+2,2x-1are in A.P. then find the value of x​

Answer 1

Step-by-step explanation:

Given that x-1,x+2,2x-1,... is an arithmetic sequence

To find the value of x in the given arithmetic sequence :

First put x=6 in the sequence x-1,x+2,2x-1,... we get

6-1,6+2,2(6)-1,...

5,8,11,...

Now verify that 5,8,11,... is an arithmetic sequence

Let , ,,...

To find the common difference d

SUbstituting the values we get

d=8-5

Therefore d=3

Substituting the values we get

d=11-8

Therefore d=3

Therefore the common difference d is 3

Therefore the sequence 5,8,11,... is an arithmetic sequence

Hence the value of x in the given arithmetic sequence x-1,x+2,2x-1,... is 6.

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Answer 2

Given :-

• A sequence of numbers, as x - 1, x + 2, 2x - 1 are in AP.

To Find :-

• Value of x.

Solution :-

Given that the sequence of numbers are in AP which means the difference between each consecutive term is the same.

Sequence: x - 1 , x + 2 , 2x - 1

Now, as discussed earlier, the difference between the second term and the first term is equal to the difference between the third term and the second term.

⇒ 2nd term - 1st term = 3rd term - 4th term

⇒ (x + 2) - (x - 1) = (2x - 1) - (x + 2)

⇒ x + 2 - x + 1 = 2x - 1 - x - 2

⇒ 2 + 1 = x - 1 - 2

⇒ 3 = x - 3

⇒ x = 6

Hence, the value of x is 6.

Some Information :-

• In an AP, the difference between each consecutive term is the same which is known as the common difference of the AP and is generally denoted by d.

• Nth term of an AP which has its first term and the common difference as d is given by, aₙ = a + (n - 1)d