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Precalculus Enhanced with Graphing Utilities

Sullivan

$Math Studyset 91影视 Explanations$ Math

6th Edition 路 1200 pages

ISBN: 9780321795465

Chapter 12: Q. 54 (page 817)

The sum of the first 46 terms of the sequence 2, -1, -4,-7, 鈥�

Short Answer

Expert verified

The sum of the first 46 terms of the sequence -3013

Step by step solution

01

Given Information

Arithmetic sequence is 2, -1, -4,-7, 鈥�

02

Difference

sequence 2, -1, -4,-7, 鈥�

first term is 2

difference is -2-2=-3

-4-(-1)=-3

d=-3

Sum formula

$S_{n} = \frac{n}{2} (2 a_{1} + (n - 1) d) w h e r e a_{1} i s t h e f i r s t t e r m d i s t h e d i f f e r e n c e b e t w e e n t h e t e r m s n i s t h e n u m b e r o f t e r m s$

03

Sum

Substitute the values in sum formula

$S_{n} = \frac{n}{2} (2 a_{1} + (n - 1) d) n = 46 b e c a u s e w e n e e d s u m f o r 46 t e r m s S_{46} = \frac{46}{2} (2 (2) + (46 - 1) (- 3)) S_{46} = 23 (4 + (45) (- 3)) S_{46} = 23 (4 - 135) S_{46} = - 3, 013$

The sum of the first 46 terms of the sequence -3013

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Most popular questions from this chapter

In Problems 61鈥�70, express each sum using summation notation.

$3 + \frac{3^{2}}{2} + \frac{3^{3}}{3} + . . . . . + \frac{3^{n}}{n}$

In Problems 71-82, find the sum of each sequence.

${鈭� (-}_{k = 1}^{24} k)$

In Problems 61鈥�70, express each sum using summation notation.

$a + a r + a r^{2} + . . . . . + a r^{n - 1}$

In Problems 17鈥�28, write down the first five terms of each sequence.

$\{b_{n}\} = \{\frac{2 n + 1}{2 n}\}$

In Problems 17鈥�28, write down the first five terms of each sequence.

$\{d_{n}\} = \{{(- 1)}^{n - 1} (\frac{n}{2 n - 1})\}$

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