What is the sum of the first 20 terms in the series 1, 5, 9, 13, 17…?

To find the sum of the first 20 terms in the series 1, 5, 9, 13, 17..., we first identify the elements of the sequence. This series is an arithmetic sequence, where the first term (a = 1) and the common difference (d = 4).

The formula for the (n)-th term of an arithmetic sequence is given by:

[

a_n = a + (n - 1) \cdot d

]

Applying this formula, the 20th term can be calculated as follows:

[

a_{20} = 1 + (20 - 1) \cdot 4 = 1 + 19 \cdot 4 = 1 + 76 = 77

]

Next, to find the sum of the first (n) terms of an arithmetic series, we can utilize the formula:

[

S_n = \frac{n}{2} \cdot (a + a_n)

]

Substituting in the known values:

• (n = 20)

• (a = 1)

• (a_{20} = 77)

Now we can