Question51-56 - Partial Sums of an Arithmetic Sequence Find the partial sum $S_{n}$ of the arithmetic sequence that satisfies the given conditions.
51. $a=3, \quad d=5, \quad n=20$

Studdy Solution

STEP 1

1. We are dealing with an arithmetic sequence.
2. The first term of the sequence is $a = 3$ .
3. The common difference between consecutive terms is $d = 5$ .
4. We need to find the sum of the first $n = 20$ terms.

STEP 2

1. Identify the formula for the partial sum of an arithmetic sequence.
2. Calculate the last term of the sequence.
3. Substitute the known values into the sum formula and solve for $S_n$ .

STEP 3

The formula for the partial sum $S_n$ of an arithmetic sequence is:
$S_n = \frac{n}{2} \times (a + l)$
where $n$ is the number of terms, $a$ is the first term, and $l$ is the last term.

STEP 4

Calculate the last term $l$ using the formula for the $n$ -th term of an arithmetic sequence:
$l = a + (n-1) \times d$
Substitute the given values:
$l = 3 + (20-1) \times 5$ $l = 3 + 19 \times 5$ $l = 3 + 95$ $l = 98$

STEP 5

Substitute the values of $n$ , $a$ , and $l$ into the partial sum formula:
$S_{20} = \frac{20}{2} \times (3 + 98)$ $S_{20} = 10 \times 101$ $S_{20} = 1010$
The partial sum $S_{20}$ of the arithmetic sequence is:
$\boxed{1010}$

Was this helpful?

Get Studdy

Scan QR code with your device to get Studdy on iOS or Android

QR code

Studdy solves anything!

Download the app

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Parents Influencer program Contact Policy Terms