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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. 52 (page 817)

In Problems 37鈥�54, find each sum.
${鈭�}_{n = 1}^{80} (\frac{1}{3} n + \frac{1}{2})$

Short Answer

Expert verified

${鈭�}_{n = 1}^{80} (\frac{1}{3} n + \frac{1}{2}) = 1120$

Step by step solution

01

Given Information

${鈭�}_{n = 1}^{80} (\frac{1}{3} n + \frac{1}{2})$

02

find out first term

${鈭�}_{n = 1}^{80} (\frac{1}{3} n + \frac{1}{2}) t o t a l o f 80 t e r m s a_{n} = \frac{1}{3} n + \frac{1}{2} t o f i n d f i r s t t e r m, r e p l a c e n = 1 a_{1} = \frac{1}{3} (1) + \frac{1}{2} = \frac{5}{6}$

03

last term

$a_{n} = \frac{1}{3} n + \frac{1}{2} n = 80 a_{80} = \frac{1}{3} (80) + \frac{1}{2} a_{80} = \frac{160}{6} + \frac{3}{6} = \frac{163}{6}$

04

Sum

apply sum formula

$S_{n} = \frac{n}{2} (a_{1} + a_{80}) S_{80} = \frac{80}{2} (a_{1} + a_{100}) S_{80} = \frac{80}{2} (\frac{5}{6} + \frac{163}{6}) S_{80} = 40 (28) S_{80} = 1120$

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Most popular questions from this chapter

Growth of a Rabbit Colony:

A colony of rabbits begins with one pair of mature rabbits, which will produce a pair of offspring (one male, one female) each month. Assume that all rabbits mature in 1 month and produce a pair of offspring (one male, one female) after 2 months. If no rabbits ever die, how many pairs of mature rabbits are there after 7 months?

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