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Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 12: Q 116 (page 1185)

Find the sum of the first 50 terms of the arithmetic sequence whose general term is given.
$a_{n} = 鈭� 4 n + 3$

Short Answer

Expert verified

The obtained sum is -4950.

Step by step solution

01

Step 1. Given Information.

The given general formula is $a_{n} = 鈭� 4 n + 3$ .

02

Step 2. Find the first and 50th terms.

Substitute 1 for n in the formula for the first term.

$\begin{array}{rcl} a_{1} & = & 鈭� 4 (1) + 3 \\ = & - 1 \end{array}$

Substitute 50 for n in the formula for the 50th term.

$\begin{array}{rcl} a_{50} & = & 鈭� 4 (50) + 3 \\ = & - 200 + 3 \\ = & - 197 \end{array}$

03

Step 3. Find the sum of 50th terms.

Use the formula of sum $S_{n} = \frac{n}{2} (a_{1} + a_{n})$ .

$\begin{array}{rcl} S_{50} & = & \frac{50}{2} (鈭� 1 鈭� 197) \\ = & 25 (鈭� 198) \\ = & 鈭� 4950 \end{array}$

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Most popular questions from this chapter

Expand the partial sum and find its value: ${鈭�}_{i = 1}^{5} 4 i$

In the following exercises, evaluate.

(a) $(\begin{array}{l} 3 \\ 1 \end{array})$ (b) $(\begin{array}{l} 9 \\ 9 \end{array})$ (c) $(\begin{array}{l} 7 \\ 0 \end{array})$ (d) $(\begin{array}{l} 5 \\ 3 \end{array})$

Write the first five terms of the sequence where the first term is $6$ and the common ratio is $r = - 4$ .

Find the eighteenth term of a sequence where the first term is 13 and the common difference is 鈭�7.

Determine if each sequence is geometric. If so indicate the common ratio.

鈸� $鈭� 150, 鈭� 30, 鈭� 15, 鈭� 5, \frac{- 5}{2}, 0, 鈥�$

鈸� $5, 10, 20, 40, 80, 160, 鈥�$

鈸� $8, 4, 2, 1, \frac{1}{2}, \frac{1}{4}, 鈥�$

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