Arithmetic Progression (A.P.)
1. In each of the following A.P., find
(a) the common difference (b) the 10th term (c) the th
term
(d) the sum of the first 10 terms (e) the sum of the first terms
(i) 1, 3, 5, 7, ... (ii) −25, −20, −15, −10, ...
(iii)10, 9, 8, 7, ... (iv) − , − , − , − , ...
2. The 6th term of an A.P. is 32 while the 10th term is 48. Find the common difference and the 21st term.
3. The 5th term of an A.P. is 10 while the 15th term is 40. Find the common difference and the 1st term.
4. Which term of the A.P. 6, 13, 20, 27, ... is 111?
5. Find the sum of all multiples of 7 between 400 and 500.
6. Find the sum of all even numbers between 70 and 150 inclusive.
7. Find the sum of all odd numbers between 101 and 201.
8. If 5, , , 71 are consecutive terms of an A.P., find the values of and .
9. The fourth term of an A.P. is 1 and the sum of the first 8 terms is 24. Find the sum of the first 3 terms
of the progression.
10. The sum of the first 8 terms of an A.P. is 56 and the sum of the first 20 terms is 260. Find the first
term and the common difference of the A.P.
11. In an arithmetic progression whose first term is – 27, the tenth term is equal to the sum of the first 9
terms. Calculate the common difference.
12. The sum of four consecutive numbers in an A.P. is 28. The product of the second and third numbers
exceeds that of the first and last by 18. Find the numbers.
13. Find the smallest number of terms of the A.P. 4, 7, 10, ... that must be taken for the sum of the terms
to exceed 1000.
14. Find the smallest number of terms of the A.P. −54, −52 , −51, −49 , ... that must be taken for the
sum of the terms to be positive.
ANSWERS :
1. (i) (a) 2 (b) 19 (c) 2 − 1 (d) 100 (e) (ii) (a) 5 (b) 20 (c) 5 − 30 (d) -25 (e) ( − 11) (iii) (a) -1
(b) 1 (c) 11 − (d) 55 (e) (21 − ) (iv) (a) − (b) −1 (c) − (d) −6 (e) − ( + 1) 2. 4, 92
3. 3, −2 4. 16th 5. 6321 6. 4510 7. 7399 8. = 27, = 49 9. -21 10. 3 , 1 11. 8 12. 2 , 5 , 8 , 11
13. 26 14. 74
1. In each of the following A.P., find
(a) the common difference (b) the 10th term (c) the th
term
(d) the sum of the first 10 terms (e) the sum of the first terms
(i) 1, 3, 5, 7, ... (ii) −25, −20, −15, −10, ...
(iii)10, 9, 8, 7, ... (iv) − , − , − , − , ...
2. The 6th term of an A.P. is 32 while the 10th term is 48. Find the common difference and the 21st term.
3. The 5th term of an A.P. is 10 while the 15th term is 40. Find the common difference and the 1st term.
4. Which term of the A.P. 6, 13, 20, 27, ... is 111?
5. Find the sum of all multiples of 7 between 400 and 500.
6. Find the sum of all even numbers between 70 and 150 inclusive.
7. Find the sum of all odd numbers between 101 and 201.
8. If 5, , , 71 are consecutive terms of an A.P., find the values of and .
9. The fourth term of an A.P. is 1 and the sum of the first 8 terms is 24. Find the sum of the first 3 terms
of the progression.
10. The sum of the first 8 terms of an A.P. is 56 and the sum of the first 20 terms is 260. Find the first
term and the common difference of the A.P.
11. In an arithmetic progression whose first term is – 27, the tenth term is equal to the sum of the first 9
terms. Calculate the common difference.
12. The sum of four consecutive numbers in an A.P. is 28. The product of the second and third numbers
exceeds that of the first and last by 18. Find the numbers.
13. Find the smallest number of terms of the A.P. 4, 7, 10, ... that must be taken for the sum of the terms
to exceed 1000.
14. Find the smallest number of terms of the A.P. −54, −52 , −51, −49 , ... that must be taken for the
sum of the terms to be positive.
ANSWERS :
1. (i) (a) 2 (b) 19 (c) 2 − 1 (d) 100 (e) (ii) (a) 5 (b) 20 (c) 5 − 30 (d) -25 (e) ( − 11) (iii) (a) -1
(b) 1 (c) 11 − (d) 55 (e) (21 − ) (iv) (a) − (b) −1 (c) − (d) −6 (e) − ( + 1) 2. 4, 92
3. 3, −2 4. 16th 5. 6321 6. 4510 7. 7399 8. = 27, = 49 9. -21 10. 3 , 1 11. 8 12. 2 , 5 , 8 , 11
13. 26 14. 74
