Advertisements
Advertisements
प्रश्न
The sum of the first n terms of an A.P. is 4n2 + 2n. Find the nth term of this A.P.
Advertisements
उत्तर
A.P. Sn = 4n2 + 2n
Sn-1 = 4(n − 1)2 + 2(n − 1)
Tn = Sn − Sn − 1
= 4n2 + 2n − 4(n − 1)2 − 2(n − 1)
= 4n2 + 2n − 4[n2 + 1 − 2n] − 2n + 2
= `4cancel(n^2) + cancel(2n) - cancel4n^2 - 4 8n - cancel2n + 2`
Tn = 8n − 2
APPEARS IN
संबंधित प्रश्न
How many terms of the A.P. 27, 24, 21, .... should be taken so that their sum is zero?
Find the sum of all natural numbers between 250 and 1000 which are exactly divisible by 3
In an AP given a = 8, an = 62, Sn = 210, find n and d.
Find the sum of first 40 positive integers divisible by 6.
Find the sum of the first 25 terms of an A.P. whose nth term is given by an = 7 − 3n
Find the sum of all natural numbers between 1 and 100, which are divisible by 3.
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
Find the sum of the following Aps:
i) 2, 7, 12, 17, ……. to 19 terms .
Write an A.P. whose first term is a and common difference is d in the following.
a = 6, d = –3
In an A.P. the 10th term is 46 sum of the 5th and 7th term is 52. Find the A.P.
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
The common difference of the A.P. is \[\frac{1}{2q}, \frac{1 - 2q}{2q}, \frac{1 - 4q}{2q}, . . .\] is
In an AP if a = 1, an = 20 and Sn = 399, then n is ______.
In an A.P., if Sn = 3n2 + 5n and ak = 164, find the value of k.
If Sn denotes the sum of first n terms of an AP, prove that S12 = 3(S8 – S4)
Find the sum of the integers between 100 and 200 that are not divisible by 9.
Find the middle term of the AP. 95, 86, 77, ........, – 247.
Find the sum of first 25 terms of the A.P. whose nth term is given by an = 5 + 6n. Also, find the ratio of 20th term to 45th term.
In a ‘Mahila Bachat Gat’, Kavita invested from the first day of month ₹ 20 on first day, ₹ 40 on second day and ₹ 60 on third day. If she saves like this, then what would be her total savings in the month of February 2020?
The nth term of an A.P. is 6n + 4. The sum of its first 2 terms is ______.
