Advertisements
Advertisements
Question
The sum of the first n terms of an A.P. is 4n2 + 2n. Find the nth term of this A.P.
Advertisements
Solution
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
RELATED QUESTIONS
Find the 9th term from the end (towards the first term) of the A.P. 5, 9, 13, ...., 185
The sum of three numbers in A.P. is –3, and their product is 8. Find the numbers
Find the sum of all natural numbers between 250 and 1000 which are exactly divisible by 3
The sum of n terms of three arithmetical progression are S1 , S2 and S3 . The first term of each is unity and the common differences are 1, 2 and 3 respectively. Prove that S1 + S3 = 2S2
Find the 20th term from the last term of the A.P. 3, 8, 13, …, 253.
If the sum of first m terms of an A.P. is the same as the sum of its first n terms, show that the sum of its first (m + n) terms is zero
Find the sum of the first 13 terms of the A.P: -6, 0, 6, 12,....
Find the sum of first 12 natural numbers each of which is a multiple of 7.
Find the sum of all natural numbers between 250 and 1000 which are divisible by 9.
If the 10th term of an AP is 52 and 17th term is 20 more than its 13th term, find the AP
The first and last terms of an AP are a and l respectively. Show that the sum of the nth term from the beginning and the nth term form the end is ( a + l ).
Write an A.P. whose first term is a and common difference is d in the following.
a = –3, d = 0
Fill up the boxes and find out the number of terms in the A.P.
1,3,5,....,149 .
Here a = 1 , d =b`[ ], t_n = 149`
tn = a + (n-1) d
∴ 149 =`[ ] ∴149 = 2n - [ ]`
∴ n =`[ ]`
The 9th term of an A.P. is equal to 6 times its second term. If its 5th term is 22, find the A.P.
If Sn denotes the sum of the first n terms of an A.P., prove that S30 = 3(S20 − S10)
If k, 2k − 1 and 2k + 1 are three consecutive terms of an A.P., the value of k is
The first three terms of an A.P. respectively are 3y − 1, 3y + 5 and 5y + 1. Then, y equals
A sum of Rs. 700 is to be paid to give seven cash prizes to the students of a school for their overall academic performance. If the cost of each prize is Rs. 20 less than its preceding prize; find the value of each of the prizes.
Find t21, if S41 = 4510 in an A.P.
The famous mathematician associated with finding the sum of the first 100 natural numbers is ______.
