List of top Mathematics Questions on Sum of First n Terms of an AP

If sum of first ten terms of an A.P. is zero with a as the first term and d, the common difference, which of the following relation is true ?

In an A.P., a = –3 and S\(_{17}\) = 357. The value of a\(_{17}\) is

How many terms of the A.P. 21, 18, 15, ... must be added to get the sum zero?

In a potato race, a bucket is placed at the starting point, which is 5 m from the first potato. The other potatoes are arranged 3 m apart in a straight line, with a total of 10 potatoes.

(i) What is the distance covered to pick up the first potato and drop it in the bucket?

For positive integers \( n \), if \( 4 a_n = \frac{n^2 + 5n + 6}{4} \) and $$ S_n = \sum_{k=1}^{n} \left( \frac{1}{a_k} \right), \text{ then the value of } 507 S_{2025} \text{ is:} $$ 

Let \[ f(x) = \lim_{n \to \infty} \sum_{r=0}^{n} \left( \frac{\tan \left( \frac{x}{2^{r+1}} \right) + \tan^3 \left( \frac{x}{2^{r+1}} \right)}{1 - \tan^2 \left( \frac{x}{2^{r+1}} \right)} \right) \] Then, \( \lim_{x \to 0} \frac{e^x - e^{f(x)}}{x - f(x)} \) is equal to:

$$ \lim_{n \to \infty} \frac{(1^2 - 1)(n-1) + (2^2 - 2)(n-2) + \ldots + ((n-1)^2 - (n-1))}{(1^3 + 2^3 + \ldots + n^3) - (1^2 + 2^2 + \ldots + n^2)} $$ is equal to: 

If \(S_n=3+7+11....\) upto \(n\) terms and \(40<\frac {6}{n(n+1)}\displaystyle\sum_{k=1}^n S_k<45\). Then \(n\) is

Let the first term of a series be \( T_1 = 6 \) and its \( r^\text{th} \) term \( T_r = 3T_{r-1} + 6^r \), \( r = 2, 3, \dots, n \). If the sum of the first \( n \) terms of this series is \[ \frac{1}{5} \left(n^2 - 12n + 39\right) \left(4 \cdot 6^n - 5 \cdot 3^n + 1\right), \] then \( n \) is equal to ______.

Let \(a_1,a_2,a_3\), ..., an, be in A. P. and \(S_n\) denotes the sum of first \(n\) terms of this A. P. is \(S_{10}\) =\(390, \frac{a_{10}}{a_{50}} =\frac{15}{7}\), then \(S_{15} -S_5 =\) _________.

Let \( S_n \) denote the sum of the first \( n \) terms of an arithmetic progression. If \( S_{20} = 790 \) and \( S_{10} = 145 \), then \( S_{15} - S_5 \) is:

The number of $3$-digit numbers, that are divisible by either $2$ or $3$ but not divisible by $7$ , is_________

The sum $1+ \frac{1^{3} +2^{3}}{1+2} + \frac{1^{3}+2^{3}+3^{3}}{1+2+3} +.... + \frac{1^{3} +2^{3}+3^{3} +....+15^{3}}{1+2+3+...+15} - \frac{1}{2} \left(1+2+3+...+15\right)$

In AP, \( a_k=5k+1 \). Find sum of first 100 terms

The sum of odd integers from 1 to 2001 is

In AP, \( a_k=5k+1 \). Find sum of first 100 terms

The sum of odd integers from 1 to 2001 is

The sum of odd integers from 1 to 2001 is:

If $a_1, a_2, a_3, a_4$ are in A.P., then $\frac{1}{\sqrt{a_1} + \sqrt{a_2}} + \frac{1}{\sqrt{a_2} + \sqrt{a_3}} + \frac{1}{\sqrt{a_3} + \sqrt{a_4}} =$

The sum $\displaystyle\sum^{10}_{r=1}(r^2 + 1) \times (r!)$ is equal to :

Find the sums given below :

1. \(7 + 10\frac 12+ 14 + ....... + 84\)
2. \(34 + 32 + 30 + ....... + 10\)
3. \(–5 + (–8) + (–11) + ....... + (–230)\)

Find the sum of the following APs:

1. \(2, 7, 12, .......,\) to \(10\) terms.
2. \(–37, –33, –29,.......,\) to \(12\) terms.
3. \(0.6, 1.7, 2.8, ......., \)to \(100\) terms.
4. \(\frac {1}{15}, \frac {1}{12}, \frac {1}{10}, .......,\) to \(11\) terms.

A small terrace at a football ground comprises of 15 steps each of which is 50 m long and built of solid concrete. Each step has a rise of \(\frac 14\) m and a tread of \(\frac 12\) m. (see Fig. 5.8). Calculate the total volume of concrete required to build the terrace.

The houses of a row are numbered consecutively from 1 to 49. Show that there is a value of x such that the sum of the numbers of the houses preceding the house numbered x is equal to the sum of the numbers of the houses following it. Find this value of x.