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
How many terms of the A.P. 18, 16, 14, .... be taken so that their sum is zero?
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.
How many terms of the series 54, 51, 48, …. be taken so that their sum is 513 ? Explain the double answer
How many terms are there in the A.P. whose first and fifth terms are −14 and 2 respectively and the sum of the terms is 40?
Find the sum of all odd natural numbers less than 50.
The sum of n natural numbers is 5n2 + 4n. Find its 8th term.
How many three-digit natural numbers are divisible by 9?
If the sum of first n terms is (3n2 + 5n), find its common difference.
Write an A.P. whose first term is a and common difference is d in the following.
a = –1.25, d = 3
Choose the correct alternative answer for the following question .
15, 10, 5,... In this A.P sum of first 10 terms is...
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.
Write the value of a30 − a10 for the A.P. 4, 9, 14, 19, ....
If the sum of n terms of an A.P. be 3n2 + n and its common difference is 6, then its first term is ______.
If the sum of n terms of an A.P. is 2n2 + 5n, then its nth term is
If the first, second and last term of an A.P. are a, b and 2a respectively, its sum is
Two A.P.'s have the same common difference. The first term of one of these is 8 and that of the other is 3. The difference between their 30th term is
Q.1
Find the sum of those integers from 1 to 500 which are multiples of 2 or 5.
[Hint (iii) : These numbers will be : multiples of 2 + multiples of 5 – multiples of 2 as well as of 5]
Find the sum:
`4 - 1/n + 4 - 2/n + 4 - 3/n + ...` upto n terms
Find the sum of first 17 terms of an AP whose 4th and 9th terms are –15 and –30 respectively.
