Question

the fifth term of an ap is 26and its tenth term is 51 find ap ​

Answer 1

Step-by-step explanation:

Given:

• 5th term of the A.P. is 26
• 10 th term of the A.P. is 51

Required to Find:

• Find the A.P.

Solution:

We know that nth term(An) of an A.P. is

An = a + (n - 1)d, where a is the first term and n is the no of terms and d is the common difference.

So,

A5 = a + (5 -1)d

=>26 = a + 4d ---------------(i)

Again,

A10 = a + (10 - 1)d

=> 51 = a + 9d ----------------(ii)

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Now,

Subtracting equation (i) from (ii) we get,

a + 9d - a - 4d = 51 - 26

=> 5d = 25

=> d = 25/5

=> d = 5

Therefore, Common Difference (d) of the given A.P. is 5

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Now, putting the value of d = 5 in equation (i), We get,

26 = a + 4*5

=> 26 - 20 = a

=> a = 6

Therefore, First Term (a) of the given A.P. is 6

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So, the required A.P. is :

6, 11, 16, 21, 26,.............

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Finding the A.P:

In the given A.P.

First Term = a = 6

Second term = a + d = 6 + 5 = 11

3 rd Term = a + 2d = 6 + 2*5 = 16

4th Term = a + 3d = 6 + 3*5 = 21

and so on....

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