NCERT Class X Chapter 5: Arithmetic Progression Exercise 5.2 Question 10

NCERT Class X Chapter 5: Arithmetic Progression Exercise 5.2 Question 10

Question:

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

Given:

Let the arithmetic progression be denoted by {an}. The 17th term (a17) exceeds the 10th term (a10) by 7. Therefore, a17 - a10 = 7

To Find:

The common difference (d) of the arithmetic progression.

Formula:

The nth term of an AP is given by an = a + (n-1)d, where 'a' is the first term and 'd' is the common difference.

Solution:

We are given that a17 - a10 = 7.

Using the formula for the nth term, we have:

a17 = a + (17-1)d = a + 16d

a10 = a + (10-1)d = a + 9d

Substituting these into the given equation:

(a + 16d) - (a + 9d) = 7

⇒ a + 16d - a - 9d = 7

⇒ 7d = 7

Solving for d:

d = 7 7 = 1

Result:

The common difference is 1.

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