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प्रश्न
The common difference of the A.P.
विकल्प
- \[\frac{1}{3}\]
- \[- \frac{1}{3}\]
−b
b
उत्तर
Let a be the first term and d be the common difference.
The given A.P. is \[\frac{1}{3}, \frac{1 - 3b}{3}, \frac{1 - 6b}{3}, . . .\]
Common difference = d = Second term − First term
= \[\frac{1 - 3b}{3} - \frac{1}{3}\]
= \[\frac{- 3b}{3} = - b\]
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संबंधित प्रश्न
The sum of n terms of three arithmetical progression are S1 , S2 and S3 . The first term of each is unity and the common differences are 1, 2 and 3 respectively. Prove that S1 + S3 = 2S2
Find the sum given below:
34 + 32 + 30 + ... + 10
Find the sum 25 + 28 + 31 + ….. + 100
Find the sum of the first 25 terms of an A.P. whose nth term is given by an = 2 − 3n.
The first and the last terms of an A.P. are 34 and 700 respectively. If the common difference is 18, how many terms are there and what is their sum?
How many numbers are there between 101 and 999, which are divisible by both 2 and 5?
Find the sum of the first n natural numbers.
First term and the common differences of an A.P. are 6 and 3 respectively; find S27.
Solution: First term = a = 6, common difference = d = 3, S27 = ?
Sn = `"n"/2 [square + ("n" - 1)"d"]` - Formula
Sn = `27/2 [12 + (27 - 1)square]`
= `27/2 xx square`
= 27 × 45
S27 = `square`
Q.10
If the last term of an A.P. of 30 terms is 119 and the 8th term from the end (towards the first term) is 91, then find the common difference of the A.P. Hence, find the sum of all the terms of the A.P.
