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Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 11: Q. 331 (page 1069)

Find the sum.
${鈭� (5 i - 21}_{i = 1}^{40})$

Short Answer

Expert verified

The sum of first $40^{t h}$ term of an arithmetic sequence is $3260$ .

Step by step solution

01

Step 1. Given information

Given expression

${鈭� (5 i - 21}_{i = 1}^{40})$

02

Step 2. Write the concept

The sum $S_{n}$ of the first n term of arithmetic sequence is

$S_{n} = \frac{n}{2} (a_{1} + a_{n})$

$a_{1} = f i r s t t e r m a_{n} = n^{t h} t e r m$

03

Step 3. Calculation

Expand the given function

${鈭� (5 i - 21}_{i = 1}^{40}) = (5 路 1 - 21) + (5 路 2 - 21) + (5 路 3 - 21) + . . . . . . + (5 路 40 - 21) = (5 - 21) + (10 - 21) + (15 - 21) + . . . . . . . . . + (200 - 21) = (- 16) + (- 11) + (- 6) + . . . . . . . . + 179 T h e r e f o r e, 1^{s t} t e r m i s - 16 a n d 40^{t h} i s 179 .$

Now, substituting the values to get final answer.

$a_{1} = - 16 a_{40} = 179 n = 40 S_{40} = \frac{40}{2} (- 16 + 179) = 20 (163) = 3260$

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Most popular questions from this chapter

In the following exercises, solve:

$6 m (12 m 鈭� 5) = 0$

Use the Quotient Property to simplify square roots.

$\sqrt{\frac{180 s^{10}}{144}}$

Factor $a^{2} - 11 a b + 10 b^{2}$

Use the Quotient Property to simplify square roots.

(a) $\sqrt{\frac{72 x^{5}}{y^{6}}}$

(b) $\sqrt[5]{\frac{96 r^{11}}{s^{5}}}$

(c) $\sqrt[6]{\frac{128 u^{7}}{v^{12}}}$

In the following exercises, write with a rational exponent.

Part (a): $\sqrt[3]{25 a}$

Part (b): $\sqrt{3 b}$

Part (c): $\sqrt[8]{40 c}$

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