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
If the sum of first 7 terms of an A.P. is 49 and that of its first 17 terms is 289, find the sum of first n terms of the A.P.
The first and the last terms of an AP are 8 and 65 respectively. If the sum of all its terms is 730, find its common difference.
A small terrace at a football field comprises 15 steps, each of which is 50 m long and built of solid concrete. Each step has a rise of `1/4` m and a tread of `1/2` m (See figure). Calculate the total volume of concrete required to build the terrace.
[Hint: Volume of concrete required to build the first step = `1/4 xx 1/2 xx 50 m^3`]
If the nth term of the A.P. 9, 7, 5, ... is same as the nth term of the A.P. 15, 12, 9, ... find n.
Which term of the AP 21, 18, 15, …… is -81?
Which term of the A.P. `20, 19 1/4, 18 1/2, 17 3/4,` ..... is the first negative term?
If (3y – 1), (3y + 5) and (5y + 1) are three consecutive terms of an AP then find the value of y.
The sum of three numbers in AP is 3 and their product is -35. Find the numbers.
Find the first term and common difference for the A.P.
`1/4,3/4,5/4,7/4,...`
Choose the correct alternative answer for the following question .
In an A.P. 1st term is 1 and the last term is 20. The sum of all terms is = 399 then n = ....
The sum of first 9 terms of an A.P. is 162. The ratio of its 6th term to its 13th term is 1 : 2. Find the first and 15th term of the A.P.
If the sum of n terms of an A.P. is 2n2 + 5n, then its nth term is
If the nth term of an A.P. is 2n + 1, then the sum of first n terms of the A.P. is
Q.2
If a = 6 and d = 10, then find S10
What is the sum of an odd numbers between 1 to 50?
In an AP if a = 1, an = 20 and Sn = 399, then n is ______.
An AP consists of 37 terms. The sum of the three middle most terms is 225 and the sum of the last three is 429. Find the AP.
The ratio of the 11th term to the 18th term of an AP is 2 : 3. Find the ratio of the 5th term to the 21st term, and also the ratio of the sum of the first five terms to the sum of the first 21 terms.
