\large{\textcolor{cyan}{\rm{Question:}}} \\ Find the sum of the first 20 terms of an arithmetic progression if the first term is 3 and the common difference is 5.​

Question

`\large{\textcolor{cyan}{\rm{Question:}}} \\` Find the sum of the first 20 terms of an arithmetic progression if the first term is 3 and the common difference is 5.​

Answer 1

We use the formula for the sum of the first n terms of an arithmetic progression:

`(n)/(2)(2a_1 + (n - 1)d)`

where $S_n$ is the sum of the first n terms, $a_1$ is the first term, $d$ is the common difference, and $n$ is the number of terms.

Substituting the given values, we have:

`_(20) = (20)/(2)(2(3) + (20 - 1)(5)) = 10(6 + 95) = \boxed{1010}`

Therefore, the sum of the first 20 terms of the arithmetic progression is 1010.

Answer 2

To find the sum of the first 20 terms of an arithmetic progression, we use the formula:

S_n = n/2[2a + (n-1)d],

where S_n is the sum of the first n terms of the arithmetic progression, a is the first term of the progression, d is the common difference and n is the number of terms.

Substituting the given values, we get:

S_20 = 20/2[2*3 + (20-1)*5]

= 10[6 + 95]

= 10(101)

= 1010

Therefore, the sum of the first 20 terms of the arithmetic progression is 1010.