Arithmetic Progression

Arithmetic Progressions

1. Write the 3^rd , 5^th and 8^th term of the sequence whose nth term is given by tn = (4n+1)/2
   
2. Show that a-b, a , a+b are three consecutive terms of an A.P.
   
3. If 2, 3k-1, 8 are in A.P. then what is the value of k?
   
4. Write first four terms of the A.p. whose first term is -1 and common difference is -2.
   
5. Find the nth term of the AP 3,5,7,9,11……. Also find its 16th term.
   
6. Which term of the A.P. 5,9,13,17,….. is 81?
   
7. Is 51 a term of the A.P. 5,8,11,14…….. ?
   
8. The sixth term of an A.P. is -10 and its 10^th term is -26. Determine the 15^th term.
   
9. If the 8^th term of an V is 31 and its 15^th term is 16 more than the 11^th term, find the A.P.
   
10. The 8^th term of an A.P. is zero. Prove that its 38^th term is triple its 18^th term.
    
11. Which term of the A.P. 24, 21, 18, 15…….. is the first negative term?
    
12. Find three terms in A.P. whose sum is 21 and product is 231?
    
13. Divide 24 in three parts such that they are in A.P. and their product is 440.
    
14. If 10 times the 10^th term of an A.P. is equal to the 15 times the 15^th term, show that its 25^th term is zero.
    
15. In an A.P. prove that t_m+n +t_m-n = 2t_m
    
16. Find the 20^th term from the end of the A.P. 3, 8, 13,……,253.
    
17. How many 2-digit numbers are divisible by 3?
    
18. How many 3-digit numbers are divisible by 7?
    
19. How many numbers between 121 and 446 are divisible by 7?
    
20. Which term of the A.P. 3, 15, 27….. will be 132 more than its 54^th term?
    
21. The fourth term of an A.P. is equal to 3 times its first term and its seventh term exceeds twice the third term by 1. Find the common difference and first term of the A.P.
    
22. Find the sum 3+11+19+……+803.
    
23. The angles of a triangle are in A.P. The greatest angle is twice the least. Find all the angles.
    
24. If the sum of first 7 terms of an A.P. is 49 and that of 17 terms is 289, find the sum of first n terms.
    
25. Find the common difference of an A.P. whose first term is 5 and sum of first four terms is half of the sum of next four terms.
    
26. If S_n = 5n² – 3, find the A.P. and also find its 20^th term.
    
27. Find four numbers in A.P. whose sum is 20 and sum of whose squares is 120.
    
28. If p<th term of an A.P. is q and qth term is p then show that its (p+q)th term is zero.
    
29. If m times the mth term of an A.P. is equal to n times the nth term and m≠n, show that its (m+n)th term is zero.
    
30. If pth, qth, rth terms of an A.P. are a,b,c respectively, then show that a(q-r)+b(r-p)+c(p-q)=0.
    
31. If mth term of an A.P. is 1/n and its nth term is 1/m, show that its (mn)th term is 1.