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.
How many terms of the AP. 9, 17, 25 … must be taken to give a sum of 636?
If the sum of the first n terms of an AP is 4n − n2, what is the first term (that is, S1)? What is the sum of the first two terms? What is the second term? Similarly, find the 3rd, the 10th, and the nth terms.
Find the sum 2 + 4 + 6 ... + 200
Find the sum of all odd natural numbers less than 50.
The 4th term of an AP is zero. Prove that its 25th term is triple its 11th term.
The fourth term of an A.P. is 11. The sum of the fifth and seventh terms of the A.P. is 34. Find its common difference.
If m times the mth term of an A.P. is eqaul to n times nth term then show that the (m + n)th term of the A.P. is zero.
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.
The first and the last terms of an A.P. are 8 and 350 respectively. If its common difference is 9, how many terms are there and what is their sum?
The sum of first seven terms of an A.P. is 182. If its 4th and the 17th terms are in the ratio 1 : 5, find the A.P.
Q.6
Find the sum of first 20 terms of an A.P. whose first term is 3 and the last term is 57.
Write the formula of the sum of first n terms for an A.P.
The first term of an AP is –5 and the last term is 45. If the sum of the terms of the AP is 120, then find the number of terms and the common difference.
Find the sum of those integers between 1 and 500 which are multiples of 2 as well as of 5.
Measures of angles of a triangle are in A.P. The measure of smallest angle is five times of common difference. Find the measures of all angles of a triangle. (Assume the measures of angles as a, a + d, a + 2d)
Find the middle term of the AP. 95, 86, 77, ........, – 247.
The sum of all two digit numbers is ______.
The sum of A.P. 4, 7, 10, 13, ........ upto 20 terms is ______.
