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