## Class 10

1.If five times the fifth term of an A.P. is equal to eight times its eighth the
term, show that its 13th term is zero.

2. Find the middle term of the A.P.  6,  13, 20, ...  .216.

3.The sum of three numbers in A.P. is 12 and sum of their cubes is 288. Find the numbers.

4. Find the sum of the first five multiples of 2.

5.What is the common difference of an A.P. which  a21 - a7 = 84.

6. How many terms of the A.P. 27, 24, 21 .... should be taken so that their sum is zero?

7.The first and last term of an A.P. are 5 and 45 respectively. If the sum of all its terms is 400, find its common difference

8. The tenth term of an A.P. is - 37 and the sum of its first  six  terms  is  -27 .  Find  the  sum  of  its  first eighterms.

9. Find the number of multiple of 9 lying between 300 and 700.

10.   If the tenth term of an A.P. is 52 and the 17th term is 20 more than the 13th term, find A.P.

11.Find the  60th  term of the A.P.  8, 10, 12, ....,  if it has     a total of 60 terms and hence find the sum of its last 10 terms.

12.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 numbers on both sides of the middle term separately.

13.The sum of the 3rd and 7th terms of an A.P. is 6 and their product is 8. Find the sum of the first 20 terms of the A.P.

14. Find the number of natural numbers between 101 and 999 which are divisible by both 2 and 5.

15. If 1 + 4 + 7 + 10+...... + x = 287, Find the value of x.

16..  Find the sum of first 24 terms of an A.P. whose nth term given by an = 3 + 2n.

17.If the ratio of the 11th term of an A.P.  to its  18th  term is 2 : 3, find the ratio of the sum of the first five term of the sum of its first 10 terms.

18.  A sum of Rs. 280 is to be used towards four prizes.   If each prize after the first is Rs. 20 less than its preceding prize, find the value of each of the prizes.

19.The 16th term of an A.P. is five times its third term. If its 10th term is 41, then find the sum of its first fifteen terms.

20.Find the sum of first seventeen terms of A.P. whose 4th  and  9th  terms are - 15  and -30  respectively.

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