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

Solution:

An arithmetic sequence has a common difference between any two consecutive terms.

The formula for n^th term of an AP is aₙ = a + (n - 1) d

Here, aₙ is the n^th term, a is the first term, d is the common difference and n is the number of terms.

a₁₇ = a + (17 - 1)d

a₁₇ = a + 16d

a₁₀ = a + (10 - 1)d

a₁₀ = a + 9d

According to the question, a₁₇ - a₁₀ = 7 (given)

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

16d - 9d = 7

7d = 7

d = 1

The common difference is 1.

☛ Check: NCERT Solutions for Class 10 Maths Chapter 5

Video Solution:

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

NCERT Solutions Class 10 Maths Chapter 5 Exercise 5.2 Question 10

Summary:

The common difference of the AP in which the 17^th term exceeds the 10^th term by 7 is 1.

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