10 - Arithmetic Progressions – 1

1.     A man repays a loan of Rs.7140 by paying Rs.40 in the first month and then increases the payment by Rs.30 every month. Find the number of installments to clear the loan.

2.     If p^th term of an AP is q and q^th term is p, prove that its r^th term is p+q-r.

3.     150 workers were engaged to finish a piece of job in a certain number of days. Four workers  dropped on the second day, four more workers dropped on third day and so on. It takes 8 more days to finish the job now. Find the number of days in which the job was completed.

4.     For an AP show that a_p + a_p+2q = 2a_p+q.

5.     The sum of first three terms of an AP is 18 and the sum of their squares is 126. Find the AP.

6.     Find the middle term of the sequence formed by all three digit numbers which leave a remainder 5 when divided by 7. Also find the sum of all the numbers on both sides of the middle term separately.

7.     The sum of first 7 terms of an AP is 182. If the fourth term and seventh term are in the ratio 1:5, find the AP.

8.     Find the values of a, b and c such that a , 7 ,b , 23 , c  are in AP.

9.     Find the 6^th term from the end of the AP 203, 210, 217, ….., 896.

10. In an AP, the sum of first 10 terms is -150 and the sum of next 10 terms is    -550. Find the AP.

11.     Find the value of the middle term of the AP -6, -2, 2, ….., 58.        

12.   If the ratio of the sum of the first n terms of two A.Ps is (7n+1):(4n+27) , then find the ratio of their 9^th terms.