Algebra - Arithematic Progression Notes & Question for ICSE Class 10 2021
Syllabus for AP
Finding their General term.
Finding Sum of their first ‘n’ terms
Notes & Points on AP
Question to Practice in AP
1. Find the general terms of
a) a=7 d=4
b) 3,6,9,12
c) a=-4 d=-7
d) 11....51,61..91
2. Find the Series of the following
a) a=18, d= 9
b) An = 2n+3
3. Find the 8th term of the A.P. whose first term is 7 and common difference is 3
4. If the common difference of an A.P. is – 3 and the 18th term is – 5, then find its first term.
5.If the first term of an A.P. is – 18 and its 10th term is zero, then find its common difference.
6. Which term of the A.P.
(i) 3, 8, 13, 18, … is 78?
(ii) 7, 13, 19, … is 205 ?
7.Determine the A.P. whose third term is 16 and the 7th term exceeds the 5th term by 12
8. Find the 31st term of an A.P. whose 11th term is 38 and 6th term is 73.
9. The 15th term of an A.P. is 3 more than twice its 7th term. If the 10th term of the A.P. is 41, find its nth term.
10. The sum of 5th and 7th terms of an A.P. is 52 and the 10th term is 46. Find the A.P.
11. The sum of 2nd and 7th terms of an A.P. is 30. If its 15th term is 1 less than twice its 8th term, find the A.P
12. In an A.P. (with usual notations) :
(i) given a = 5, d = 3, an = 50, find n and Sn
(ii) given a = 7, a13 = 35, find d and S13
(iii) given d = 5, S9 = 75, find a and a9
(iv) given a = 8, an = 62, Sn = 210, find n and d
(v) given a = 3, n = 8, S = 192, find d.
13. The first term of an A.P. is 5, the last term is 45 and the sum is 400. Find the number of terms and the common difference.
14. The first and the last terms of an A.P. are 17 and 350 respectively. If the common difference is 9, how many terms are there and what is their sum?
15. Find the sum of first 22 terms, of an A.P. in which d = 7 and a22 is 149.
16. If the sum of first 6 terms of an A.P. is 36 and that of the first 16 terms is 256, find the sum of first 10 terms.
17.In an A.P., the sum of its first n terms is 6n – n². Find is 25th term.
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