Find the sum of the following arithmetic progressions: $ 50,46,42, \ldots $ to 10 terms
Given:
Given A.P. is \( 50,46,42, \ldots \)
To do:
We have to find the sum of the given A.P. to 10 terms.
Solution:
Here, \( a=50, d=46-50=-4 \) and \( n=10 \)
We know that,
\( S_{n}=\frac{n}{2}[2 a+(n-1) d] \)
\( \therefore S_{10}=\frac{10}{2}[2 \times 50+(10-1) \times(-4)] \)
\( =5(100+9 \times(-4)]=5[100-36] \)
\( =5 \times 64=320 \)
The sum of the given A.P. to 10 terms is $320$.
Related Articles
- Find the sum of the following arithmetic progressions: \( 1,3,5,7, \ldots \) to 12 terms
- Find the sum of the following arithmetic progressions:\( 41,36,31, \ldots \) to 12 terms
- Find the sum of the following arithmetic progressions:\( -26,-24,-22, \ldots \) to 36 terms.
- Find the sum of the following arithmetic progressions:\( a+b, a-b, a-3 b, \ldots \) to 22 terms
- Find the sum of the following arithmetic progressions:\( 3, \frac{9}{2}, 6, \frac{15}{2}, \ldots \) to 25 terms
- Find the sum of the following arithmetic progressions:\( (x-y)^{2},\left(x^{2}+y^{2}\right),(x+y)^{2}, \ldots, \) to \( n \) terms
- Find out which of the following sequences are arithmetic progressions. For those which are arithmetic progressions, find out the common difference.\( 3,6,12,24, \ldots . \)
- Find the sum of the following arithmetic progressions:\( \frac{x-y}{x+y}, \frac{3 x-2 y}{x+y}, \frac{5 x-3 y}{x+y}, \ldots \) to \( n \) terms
- Find the 12th term from the end of the following arithmetic progressions:$1, 4, 7, 10, …, 88$
- Find the common difference and write the next four terms of each of the following arithmetic progressions :$1, -2, -5, -8, ……..$
- Find the common difference and write the next four terms of each of the following arithmetic progressions :$0, -3, -6, -9, ……$
- For what value of n, the nth terms of the arithmetic progressions $63, 65, 67,…$ and $3, 10, 17, …$ are equal?
- Find the common difference and write the next four terms of each of the following arithmetic progressions :$-1, \frac{1}{4}, \frac{3}{2}, ……..$
- Find the common difference and write the next four terms of each of the following arithmetic progressions :$-1, -\frac{5}{6}, -\frac{2}{3}, ………..$
- Find the 12th term from the end of the following arithmetic progressions:$3, 8, 13,…, 253$
Kickstart Your Career
Get certified by completing the course
Get Started