Question

find 100th term of an AP whose 3rd term is 5 and 7th term is 9​

Answer 1

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Answer 2

Given,

3rd term of an AP is 5 and the 7th term of an AP is 9.

To find,

100th term of an AP

Solution,

a is denoted by the first term of an AP and d is the common difference of an AP.

• 3rd term of an AP can be represented by a+2d.

• Similarly, the 7th term of an AP can be represented by a+6d.

Now,

⇒   a+2d=5 and a+6d=9

⇒   a=5-2d

Now put the value of a in a+6d.

⇒   5-2d+6d=9

⇒   5+4d=9

⇒   4d=9-5

⇒   4d=4

⇒   d=1

Here, we have found the common difference of the AP that is = 1.

⇒   a = 5-2d

⇒   a = 5-2(1)

⇒   a = 5-2

⇒   a = 3

The first term of the AP is a = 1.

Therefore, 100th term of an AP is =  a+99d.

⇒   a100= a + 99d

⇒   a100= 3 + 99(1)

⇒   a100 = 102.

Therefore, 100th term of an AP is a100 = 102.