Question 14 of 44beginner🔧 ApplyShort Answer2 marks

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

Correct Answer

The common difference is 1.

Exercise: EXERCISE 5.2 | Q: 10 | (Page Page 14)
For More Understanding

Explanation

This is a straightforward application of the nth term formula of an AP. The key insight is that when we subtract two terms of an AP, the first term 'a' gets eliminated, leaving only the common difference multiplied by the difference in position numbers.

Solution Steps

  1. Step 1: Let the first term be 'a' and common difference be 'd'.

  2. Step 2: Using the nth term formula an=a+(n−1)da_n = a + (n-1)d, we get: 17th term a17=a+16da_{17} = a + 16d and 10th term a10=a+9da_{10} = a + 9d.

  3. Step 3: According to the question, a17−a10=7a_{17} - a_{10} = 7

  4. Step 4: Substituting the values: (a+16d)−(a+9d)=7(a + 16d) - (a + 9d) = 7

  5. Step 5: Simplifying: 7d=77d = 7, therefore d = 1.

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