The 17th term of an AP exceeds its 10th term by 7. Find the common difference.
An arithmetic sequence has a common difference between any two consecutive terms.
The formula for nth term of an AP is aₙ = a + (n - 1) d
Here, aₙ is the nth 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.
17th term of an AP exceeds its 10th term by 7. Find the common difference
NCERT Solutions Class 10 Maths Chapter 5 Exercise 5.2 Question 10
The common difference of the AP in which the 17th term exceeds the 10th term by 7 is 1.
☛ Related Questions:
- Which term of the AP 3,15,27,39... will be 132 more than its 54th term?
- Two APs have the same common difference. The difference between their 100th term is 100, what is the difference between their 1000th terms?
- How many three-digit numbers are divisible by 7?
- How many multiples of 4 lie between 10 and 250?