Class 11th A.P.

1. If (m + 1)th term of an A.P. is twice the (n + 1)th term, prove that (3m + 1)th term is twice the (m + n + 1)th term. 

2. The sum of three terms of an A.P. is 21 and the product of the first and the third terms exceeds the second term by 6, find three terms. 

3. The angles of a quadrilateral are in A.P. whose common difference is 10º. Find the angles. 

4. Find the four numbersin A.P., whose sum is 50 and in which the greatest number is 4 times the least. 

5. Find the sum of the following arithmetic progressions : 

(i) a + b, a-b, a-3b, .... to 22 terms 

(ii) (x-y)2, (x2 + y2), (x + y)2, .... to n terms

6. In an A.P., if the 5th and 12th terms are 30 and 65 respectively, what is the sum of first 20 terms. 

7. Find : 

(i) 10th term of the A.P. 1, 4, 7, 10, .... 

(ii) 18th term of the A.P. .... 

(iii) nth term of the A.P. 13, 8, 3,-2, .... 

8. (i) Which term of the A.P. 3, 8, 13, .... is 248 ? 

(ii) Which term of the A.P. 84, 80, 76, .... is 0 ? 

(iii) Which term of the A.P. 4, 9, 14, .... is 254 ? 

9. (i) Is 68 a term of the A.P. 7, 10, 13, .... ? (ii) Is 302 a term of the A.P. 3, 8, 13, .... ? 

10.(i) How many terms are there in the A.P. 7, 10, 13, .... 43 ?

11.The 10th and 18th terms of an A.P. are 41 and 73 respectively. Find 26th term. 

12.If 10 times the 10th term of an A.P. is equal to 15 times the 15th term, show that 25th term of the A.P. is zero. 

13.The 6th and 17th terms of an A.P. are 19 and 41 respectively, find the 40th term. 

14.Find the sum of all odd numbers between 100 and 200. 

15.Find the sum of all integers between 84 and 719, which are multiples of 5. 

16.Find the sum of all integers between 50 and 500 which are divisible by7.

18.The general term of a sequence is given by an =-4n + 15. Is the sequence an A.P. ? If so, find its 15th term and the common difference. 

19.The first term of an A.P. is 5, the common difference is 3 and the last term is 80; find the number of terms. 

20.If the term of a sequence is given by , write down its first five terms. 

21.A sequence is defined by , Show that first three terms of the sequence are zero and all other terms are positive. 

22.Show that each of the following sequence is an A.P. Also find the common difference,

75.If n A.M.s are inserted between two numbers, prove that the sum of the means equidistant from the beginning and the end is constant. 

76.A man arranges to pay off a debt of Rs. 3600 by 40 annual instalments which form an arithmetic series. When 30 of the instalments are paid, he dies leaving one-third of the debt unpaid, find the value of the first instalment. 

77.A man is employed to count Rs. 10710. He counts at the rate of Rs 180 per minute for half an hour. After this he counts at the rate of Rs. 3 lessvery minute than the preceding minute. Find the time taken by him to count the entire amount. 

78.A farmer buys a used tractor for Rs. 12000. He pays Rs. 6000 cash and agrees to pay the balance in annual instalments of Rs. 500 plus 12% interest on the unpaid amount. How much the tractor cost him? 

79.The income of a person is Rs. 300, 000 in the firstyear and he receives an increase of Rs. 10000 to his income per year for the next 19 years. Find the total amount, he received in 20 years.