Advertisements
Advertisements
प्रश्न
If the sum of n terms of an A.P. is 2n2 + 5n, then its nth term is
पर्याय
4n − 3
3n − 4
4n + 3
3n + 4
Advertisements
उत्तर
Here, the sum of first n terms is given by the expression,
Sn = 2n2 + 5n
We need to find the nth term.
So we know that the nthterm of an A.P. is given by,
an = Sn - Sn-1
So,
`a_n = (2n^2 + 5n) - [2(n-1)^2 + 5 (n-1)]`
Using the property,
( a - b)2 = a2 + b2 - 2ab
We get,
`a_n = (2n^2 + 5n) - [2(n^2 + 1 - 2n) + 5 (n-1)]`
= (2n2 + 5n) +- (2n2 + 2 - 4n + 5n - 5)
= 2n2 + 5n - 2n2 - 2 + 4n - 5n + 5
= 4n + 3
Therefore, an = 4n + 3
APPEARS IN
संबंधित प्रश्न
Ramkali required Rs 2,500 after 12 weeks to send her daughter to school. She saved Rs 100 in the first week and increased her weekly saving by Rs 20 every week. Find whether she will be able to send her daughter to school after 12 weeks.
What value is generated in the above situation?
If Sn denotes the sum of first n terms of an A.P., prove that S30 = 3[S20 − S10]
How many terms of the series 54, 51, 48, …. be taken so that their sum is 513 ? Explain the double answer
Find the sum of the following APs.
0.6, 1.7, 2.8, …….., to 100 terms.
In an AP given a3 = 15, S10 = 125, find d and a10.
Find the sum to n term of the A.P. 5, 2, −1, −4, −7, ...,
Find the sum of all integers between 50 and 500, which are divisible by 7.
If (3y – 1), (3y + 5) and (5y + 1) are three consecutive terms of an AP then find the value of y.
Rs 1000 is invested at 10 percent simple interest. Check at the end of every year if the total interest amount is in A.P. If this is an A.P. then find interest amount after 20 years. For this complete the following activity.
If the first, second and last term of an A.P. are a, b and 2a respectively, its sum is
The nth term of an A.P., the sum of whose n terms is Sn, is
If Sn denote the sum of n terms of an A.P. with first term a and common difference dsuch that \[\frac{Sx}{Skx}\] is independent of x, then
Q.14
The sum of first 15 terms of an A.P. is 750 and its first term is 15. Find its 20th term.
How many terms of the A.P. 24, 21, 18, … must be taken so that the sum is 78? Explain the double answer.
Find the common difference of an A.P. whose first term is 5 and the sum of first four terms is half the sum of next four terms.
The sum of the first 2n terms of the AP: 2, 5, 8, …. is equal to sum of the first n terms of the AP: 57, 59, 61, … then n is equal to ______.
If the numbers n - 2, 4n - 1 and 5n + 2 are in AP, then the value of n is ______.
In an A.P., if Sn = 3n2 + 5n and ak = 164, find the value of k.
