Question

The 17th term of an AP exceeds its 10th term by 7. Find the common difference.

NCERT Class X
Mathematics - Mathematics

Chapter _ARITHMETIC PROGRESSIONS

Answer 1

Solution :

Let a be the first term and d the common difference.

It is given       $a_{17} - a_{10} = 7$

⇒ (a + 16d) - (a + 9d) = 7

⇒                          7d = 7  

⇒                            d = 1

Thus, the common difference is 7.

Answer 2

Given,

In an A.P.,

17th term - 10th term = 7

To find,

The common difference of the A.P.

Solution,

We can simply solve this mathematical problem using the following process:

Let us assume that the first term of the given A.P. is a and its common difference is d.

Mathematically,

For an A.P. with the first term a and common difference d, its n-th term can be represented as;

n-th term of the A.P.= An = a + (n-1)d

Now,

17th term - 10th term = 7

=> {a + (17-1)d} - {a + (10-1)d} = 7

=> a + 16d - a - 9d = 7

=> 7d = 7

=> d = 1

Hence, the common difference of the A.P. is 1.