Advertisements
Advertisements
प्रश्न
If the second term and the fourth term of an A.P. are 12 and 20 respectively, then find the sum of first 25 terms:
Advertisements
उत्तर
For an A.P. t2 = 12 and t4 = 20
To find : S25 = ?
∴ tn = a+(n-1)d
∴ t2 = a+(2-1)d
∴ 12 = a + d .....eq(1)
∴ t4 = a + (4 - 1)d
∴ 20 = a + 3d ....eq(2)
Substracting eq(i) from eq(ii)
a + 3d = 20
`(a + d = 12)/(2d = 8)`
`"d" = 8/2`
∴ d = 4
Substituting d = 4 in eq (i)
a + d = 12
∴ a + 4 = 12
∴ a = 12 - 4
∴ a = 8
`"S"_"n" = "n"/2 ["2a" + ("n" - 1)"d"]`
`therefore "S"_25 = 25/2 [2(8) + (25 - 1)(4)]`
`= 25/2 [16 + 24(4)]`
`= 25/2[16 + 96]`
`= 25/2 xx 112`
= 1400
The sum of first 25 terms is 1400.
APPEARS IN
संबंधित प्रश्न
In an AP given a = 3, n = 8, Sn = 192, find d.
Find the sum of the following arithmetic progressions: 50, 46, 42, ... to 10 terms
Find the sum of n terms of an A.P. whose nth terms is given by an = 5 − 6n.
In an A.P., if the 5th and 12th terms are 30 and 65 respectively, what is the sum of first 20 terms?
In an A.P., the sum of first n terms is `(3n^2)/2 + 13/2 n`. Find its 25th term.
The 7th term of an AP is –4 and its 13th term is –16. Find the AP.
If 10 times the 10th term of an AP is equal to 15 times the 15th term, show that its 25th term is zero.
If 18, a, (b – 3) are in AP, then find the value of (2a – b).
If the sum of first p terms of an AP is (ap2 + bp), find its common difference.
In an A.P. the 10th term is 46 sum of the 5th and 7th term is 52. Find the A.P.
If Sn denotes the sum of the first n terms of an A.P., prove that S30 = 3(S20 – S10).
The given terms are 2k + 1, 3k + 3 and 5k − 1. find AP.
Q.2
Q.4
Q.5
Q.7
Q.20
In an A.P. (with usual notations) : given a = 8, an = 62, Sn = 210, find n and d
Find the sum of those integers between 1 and 500 which are multiples of 2 as well as of 5.
The students of a school decided to beautify the school on the Annual Day by fixing colourful flags on the straight passage of the school. They have 27 flags to be fixed at intervals of every 2 m. The flags are stored at the position of the middle most flag. Ruchi was given the responsibility of placing the flags. Ruchi kept her books where the flags were stored. She could carry only one flag at a time. How much distance did she cover in completing this job and returning back to collect her books? What is the maximum distance she travelled carrying a flag?
