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
If the sum of the first n terms of an A.P. is `1/2`(3n2 +7n), then find its nth term. Hence write its 20th term.
Determine the A.P. whose 3rd term is 16 and the 7th term exceeds the 5th term by 12.
In an AP: Given a = 5, d = 3, an = 50, find n and Sn.
In an AP given a = 8, an = 62, Sn = 210, find n and d.
In a potato race, a bucket is placed at the starting point, which is 5 m from the first potato and other potatoes are placed 3 m apart in a straight line. There are ten potatoes in the line.
A competitor starts from the bucket, picks up the nearest potato, runs back with it, drops it in the bucket, runs back to pick up the next potato, runs to the bucket to drop it in, and she continues in the same way until all the potatoes are in the bucket. What is the total distance the competitor has to run?
[Hint: to pick up the first potato and the second potato, the total distance (in metres) run by a competitor is 2 × 5 + 2 ×(5 + 3)]
The 4th term of an AP is 11. The sum of the 5th and 7th terms of this AP is 34. Find its common difference
Find the three numbers in AP whose sum is 15 and product is 80.
If 18, a, (b - 3) are in AP, then find the value of (2a – b)
Write the next term for the AP` sqrt( 8), sqrt(18), sqrt(32),.........`
The first term of an AP is p and its common difference is q. Find its 10th term.
Find the first term and common difference for the following A.P.:
5, 1, –3, –7, ...
If the 9th term of an A.P. is zero then show that the 29th term is twice the 19th term?
The sum of n terms of two A.P.'s are in the ratio 5n + 9 : 9n + 6. Then, the ratio of their 18th term is
In an A.P. (with usual notations) : given d = 5, S9 = 75, find a and a9
In an A.P. sum of three consecutive terms is 27 and their products is 504. Find the terms. (Assume that three consecutive terms in an A.P. are a – d, a, a + d.)
The sum of the first 15 multiples of 8 is ______.
If the first term of an AP is –5 and the common difference is 2, then the sum of the first 6 terms is ______.
Sum of 1 to n natural number is 45, then find the value of n.
In a ‘Mahila Bachat Gat’, Kavita invested from the first day of month ₹ 20 on first day, ₹ 40 on second day and ₹ 60 on third day. If she saves like this, then what would be her total savings in the month of February 2020?
The sum of 41 terms of an A.P. with middle term 40 is ______.
