Advertisements
Advertisements
प्रश्न
If the nth term of an A.P. is 2n + 1, then the sum of first n terms of the A.P. is
विकल्प
n(n − 2)
n(n + 2)
n(n + 1)
n(n − 1)
Advertisements
उत्तर
Here, we are given an A.P. whose nth term is given by the following expression, `a_n = 2n + 1`. We need to find the sum of first n terms.
So, here we can find the sum of the n terms of the given A.P., using the formula, `S_n = ( n/2) ( a + l) `
Where, a = the first term
l = the last term
So, for the given A.P,
The first term (a) will be calculated using n = 1 in the given equation for nth term of A.P.
a = 2 ( 1) + 1
= 2 + 1
= 3
Now, the last term (l) or the nth term is given
l = an = 2n + 1
So, on substituting the values in the formula for the sum of n terms of an A.P., we get,
`S_n = (n /2) [(3) + 2n + 1]`
`= ( n/2) [ 4 + 2n]`
`= ( n/2) (2) (2 + n) `
= n ( 2 + n)
Therefore, the sum of the n terms of the given A.P. is `S_n = n (2 + n)` .
APPEARS IN
संबंधित प्रश्न
Find the sum of first 51 terms of an AP whose second and third terms are 14 and 18 respectively.
Show that a1, a2,..., an... form an AP where an is defined as below:
an = 3 + 4n
Also, find the sum of the first 15 terms.
A spiral is made up of successive semicircles, with centres alternately at A and B, starting with centre at A of radii 0.5, 1.0 cm, 1.5 cm, 2.0 cm, .... as shown in figure. What is the total length of such a spiral made up of thirteen consecutive semicircles? (Take `pi = 22/7`)
[Hint: Length of successive semicircles is l1, l2, l3, l4, ... with centres at A, B, A, B, ... respectively.]
Find the sum of the following arithmetic progressions:
a + b, a − b, a − 3b, ... to 22 terms
Show that the sum of all odd integers between 1 and 1000 which are divisible by 3 is 83667.
Find the sum of all 3 - digit natural numbers which are divisible by 13.
In an A.P., the sum of first n terms is `(3n^2)/2 + 13/2 n`. Find its 25th term.
Is 184 a term of the AP 3, 7, 11, 15, ….?
The 7th term of the an AP is -4 and its 13th term is -16. Find the AP.
Divide 24 in three parts such that they are in AP and their product is 440.
Find the first term and common difference for the following A.P.:
5, 1, –3, –7, ...
Two A.P.’s are given 9, 7, 5, ... and 24, 21, 18, ... If nth term of both the progressions are equal then find the value of n and nth term.
A man is employed to count Rs 10710. He counts at the rate of Rs 180 per minute for half an hour. After this he counts at the rate of Rs 3 less every minute than the preceding minute. Find the time taken by him to count the entire amount.
Write the common difference of an A.P. whose nth term is an = 3n + 7.
For what value of p are 2p + 1, 13, 5p − 3 are three consecutive terms of an A.P.?
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 \[\frac{S_1}{S_2} =\]
Q.1
If the sum of the first four terms of an AP is 40 and that of the first 14 terms is 280. Find the sum of its first n terms.
Find the sum of numbers between 1 to 140, divisible by 4
Show that the sum of an AP whose first term is a, the second term b and the last term c, is equal to `((a + c)(b + c - 2a))/(2(b - a))`
