Question

sum of the series 5,10,15,...............,500 is​

Answer 1

Answer:

Sum of the series 5,10,15,...............,500 is​ 25,250

Explanation:

Arthemic Expresion a, a+d, a+2d............ a+(n-1)d

Series- 5,10,15....500

Here, a=5

d=$a_{2}-a_{1}$

d=10-5

d=5

n=100

$S_{n} = \frac{n}{2}(2a+(n-1)d)$

$=\frac{100}{2} (2*5+(100-1)5)$

$=50(10+495)$

=50(505)

= 25,250

SPJ2

Answer 2

Concept

An arithmetic sequence or progression is a number sequence in which the second number is obtained by adding a fixed number to the first one for every pair of consecutive terms. If the first term, common difference, and total terms are known for an AP, the sum of the first n terms can be calculated. The arithmetic progression sum formula is given below:

Consider an AP with "n" terms.

S  = (n/2) * (a₁ + aₙ), where a₁ is first term, aₙ is last term and n is the number of terms.

Given

The given AP series is 5, 10, 15,..., 500.

Find

We have to find the value of the sum of the given AP series.

Solution

Here, the first term of the given AP series is = a₁ = 5.

The last term is = aₙ = 500.

Number of terms = n = 100

The sum = S = (100/2) * (5 + 500) = 50 * 505 = 25250

Hence, the value of C the sum of the series is 25250.

#SPJ2