# Class 10 – Arithmetic Progressions – Important Questions

Arithmetic Progressions – Important Questions

1. Show that the sequence defined by tn = 4n + 7 is an A.P.
2. Find the number of terms for given AP: 7, 13, 19, 25, ……, 205.
3. The 7th term of an AP is 32 and its 13th term is 62. Find AP.
4. Find the sum of all two digit odd positive numbers.
5. Find the value of ‘X’ for AP. 1+6+11+16+………+X = 148.
6. Find the 10th term from the end of the AP 8, 10, 12,…..,126.
7. The sum of three numbers of AP is 3 and their product is -35. Find the numbers.
8. A man repays a loan of Rs 3250 by paying Rs 20 in the first month and then increase the payment by Rs 15 every month. How long will it take him to clear the loan?
9. The ratio of the sums of m and n terms of an AP is m2 : n2 . Show that the ratio of the mth and nth term is (2m – 1):(2n – 1).
10. In an AP, the sum of first n terms is 3n2/2 + 5n/2, Find its 25th term.
11. Find the sum of first 10 multiples of 3.
12. If m times mth term of an AP is equal to n times its nth term and m is not equal to n, show that (m + n)th term is 0.
13. The sum of first 3 terms in an AP is 18. If the product of the first and the third term is 5 times the common difference, find the three numbers.