Math, asked by manasikoyal, 2 months ago

10, a, b, 22.are in AP then the value of a is​

Answers

Answered by ShraddhaKhanna
1

as a, a-2 and 3a are in AP

∴ a−2−a=3a−(a−2)

⇒ 2(a−2)=a+3a

⇒2a−4=4a

⇒2a=−4

⇒a=−2

Arithmetic progression or arithmetic sequence (AP) is a number sequence in which the difference between consecutive terms is constant. The sequence 5, 7, 9, 11, 13, 15,..., for example, is an arithmetic progression with a common difference of 2.

An arithmetic sequence is one that has the following elements: a, a + d, a + 2d, a + 3d, a + 4d,... The first term is a, and the common difference of the sequence is d. An arithmetic sequence's nth term is given by a = a + (n - 1)d.

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Answered by pulakmath007
1

The value of a = 14

Given :

10 , a , b , 22 are in AP

To find :

The value of a

Concept :

The nth term of an AP is

aₙ = a + (n - 1 )d.

a = first term

aₙ = nth term

d = common difference.

Solution :

Step 1 of 2 :

Find the common difference of the AP

Here it is given that 10 , a , b , 22 are in AP

First term = 10

4th term = 22

Let common difference = d

10 + (4 - 1)d = 22

⇒ 10 + 3d = 22

⇒ 3d = 12

⇒ d = 12/3

⇒ d = 4

Common Difference = 4

Step 2 of 2 :

Find the value of a

∴ a

= 2nd term of the AP

= 1st term + Common difference

= 10 + 4

= 14

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