Advertisements
Advertisements
प्रश्न
Find the sum of the following arithmetic progressions:
3, 9/2, 6, 15/2, ... to 25 terms
उत्तर
In the given problem, we need to find the sum of terms for different arithmetic progressions. So, here we use the following formula for the sum of n terms of an A.P.,
`S_n = n/2[2a + (n -1)d]`
Where; a = first term for the given A.P
d = common difference of the given A.P.
n = number of terms
3, 9/2, 6, 15/2, ... to 25 terms
Common difference of the A.P. (d) = `a_2 - a_1`
`= 9/2 - 3`
`= (9 - 6)/2`
`= 3/2`
Number of terms (n) = 25
The first term for the given A.P. (a) = 3
So, using the formula we get,
`S_25 = 25/2 [2(3) +(25 - 1)(3/2)]`
`= (25/2)[6 + (25)(3/2)]`
`= (25/2)[6 + (72/2)]`
`= (25/2) [42]`
= 525
On further simplifying we get
`S_25 = 252`
Therefore the sum of first 25 term for the given A.P. is 525
APPEARS IN
संबंधित प्रश्न
If the sum of the first n terms of an A.P. is `1/2`(3n2 +7n), then find its nth term. Hence write its 20th term.
The 19th term of an AP is equal to 3 times its 6th term. If its 9th term is 19, find the AP.
If the pth term of an AP is q and its qth term is p then show that its (p + q)th term is zero
If (2p – 1), 7, 3p are in AP, find the value of p.
The sum of the first n terms in an AP is `( (3"n"^2)/2 +(5"n")/2)`. Find the nth term and the 25th term.
Choose the correct alternative answer for the following question .
First four terms of an A.P. are ....., whose first term is –2 and common difference is –2.
Simplify `sqrt(50)`
Let Sn denote the sum of n terms of an A.P. whose first term is a. If the common difference d is given by d = Sn − kSn−1 + Sn−2, then k =
The sum of first 20 odd natural numbers is
The common difference of the A.P.
