Advertisements
Advertisements
प्रश्न
Find the sum of first n natural numbers.
Advertisements
उत्तर
The first n natural numbers are:
1, 2, 3, 4...
a = 1, d = 1, Total terms = n
\[S_n = \frac{n}{2}\left[ 2a + (n - 1)d \right]\]
\[ \Rightarrow S_n = \frac{n}{2}\left[ 2 \times 1 + (n - 1)1 \right]\]
\[ \Rightarrow S_n = \frac{n}{2}\left[ 2 + (n - 1)1 \right]\]
\[ \Rightarrow S_n = \frac{n}{2}\left[ n + 1 \right]\]
APPEARS IN
संबंधित प्रश्न
In an A.P., if pth term is 1/q and qth term is 1/p, prove that the sum of first pq terms is 1/2 (pq + 1) where `p != q`
If the sum of first p terms of an A.P. is equal to the sum of the first q terms, then find the sum of the first (p + q) terms.
Find the sum of all numbers between 200 and 400 which are divisible by 7.
Shamshad Ali buys a scooter for Rs 22000. He pays Rs 4000 cash and agrees to pay the balance in annual installment of Rs 1000 plus 10% interest on the unpaid amount. How much will the scooter cost him?
Let < an > be a sequence defined by a1 = 3 and, an = 3an − 1 + 2, for all n > 1
Find the first four terms of the sequence.
Show that the following sequence is an A.P. Also find the common difference and write 3 more terms in case.
3, −1, −5, −9 ...
If the sequence < an > is an A.P., show that am +n +am − n = 2am.
If 9th term of an A.P. is zero, prove that its 29th term is double the 19th term.
Find the 12th term from the following arithmetic progression:
3, 5, 7, 9, ... 201
The 4th term of an A.P. is three times the first and the 7th term exceeds twice the third term by 1. Find the first term and the common difference.
Find the second term and nth term of an A.P. whose 6th term is 12 and the 8th term is 22.
The first and the last terms of an A.P. are a and l respectively. Show that the sum of nthterm from the beginning and nth term from the end is a + l.
Find the sum of the following arithmetic progression :
\[\frac{x - y}{x + y}, \frac{3x - 2y}{x + y}, \frac{5x - 3y}{x + y}\], ... to n terms.
Find the sum of the following serie:
(a − b)2 + (a2 + b2) + (a + b)2 + ... + [(a + b)2 + 6ab]
Find the sum of first n odd natural numbers.
Find the sum of all odd numbers between 100 and 200.
Find the sum of all integers between 50 and 500 which are divisible by 7.
Find the sum of all two digit numbers which when divided by 4, yields 1 as remainder.
The sums of first n terms of two A.P.'s are in the ratio (7n + 2) : (n + 4). Find the ratio of their 5th terms.
If a2, b2, c2 are in A.P., prove that \[\frac{a}{b + c}, \frac{b}{c + a}, \frac{c}{a + b}\] are in A.P.
If a, b, c is in A.P., prove that:
a2 + c2 + 4ac = 2 (ab + bc + ca)
If a, b, c is in A.P., prove that:
a3 + c3 + 6abc = 8b3.
A man arranges to pay off a debt of Rs 3600 by 40 annual instalments which form an arithmetic series. When 30 of the instalments are paid, he dies leaving one-third of the debt unpaid, find the value of the first instalment.
In a cricket team tournament 16 teams participated. A sum of ₹8000 is to be awarded among themselves as prize money. If the last place team is awarded ₹275 in prize money and the award increases by the same amount for successive finishing places, then how much amount will the first place team receive?
If the sum of n terms of an AP is 2n2 + 3n, then write its nth term.
If log 2, log (2x − 1) and log (2x + 3) are in A.P., write the value of x.
If four numbers in A.P. are such that their sum is 50 and the greatest number is 4 times the least, then the numbers are
If, S1 is the sum of an arithmetic progression of 'n' odd number of terms and S2 the sum of the terms of the series in odd places, then \[\frac{S_1}{S_2}\] =
The first term of an A.P. is a, the second term is b and the last term is c. Show that the sum of the A.P. is `((b + c - 2a)(c + a))/(2(b - a))`.
If there are (2n + 1) terms in an A.P., then prove that the ratio of the sum of odd terms and the sum of even terms is (n + 1) : n
If a, b, c, d are four distinct positive quantities in A.P., then show that bc > ad
If the sum of n terms of an A.P. is given by Sn = 3n + 2n2, then the common difference of the A.P. is ______.
Any term of an A.P. (except first) is equal to half the sum of terms which are equidistant from it.
If a1, a2, a3, .......... are an A.P. such that a1 + a5 + a10 + a15 + a20 + a24 = 225, then a1 + a2 + a3 + ...... + a23 + a24 is equal to ______.
If 100 times the 100th term of an A.P. with non zero common difference equals the 50 times its 50th term, then the 150th term of this A.P. is ______.
The number of terms in an A.P. is even; the sum of the odd terms in lt is 24 and that the even terms is 30. If the last term exceeds the first term by `10 1/2`, then the number of terms in the A.P. is ______.
