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Intermediate Algebra

OPENSTAX

$Math Studyset Vaia Explanations$ Math

OER 2017 Edition · 1346 pages

ISBN: 9780998625720

Chapter 12: Q 93. (page 1184)

Find the sixteenth term of a sequence where the first term is 11 and the common difference is −6.

Short Answer

Expert verified

-79

Step by step solution

01

Step 1. Given Information.

The first term is 11 and the common difference is −6.

02

Step 2. Formula used.

Write the formula of an arithmetic sequence.

$a_{n} = a_{1} + (n - 1) d$

Where a₁ is the first term and d is a common difference.

03

Step 3. Find the sixteenth term.

Substitute 11 for the first term, -6 for d, and 16 for nin the above formula.

$\begin{array}{rcl} a_{16} & = & 11 + (16 - 1) (- 6) \\ = & 11 + (15) (- 6) \\ = & 11 - 90 \\ = & - 79 \end{array}$

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Most popular questions from this chapter

In the following exercises, evaluate.

(a) $(\begin{array}{l} 4 \\ 1 \end{array})$ (b) $(\begin{array}{l} 5 \\ 5 \end{array})$ (c) $(\begin{array}{l} 8 \\ 0 \end{array})$ (d) $(\begin{array}{l} 11 \\ 9 \end{array})$

In the following exercises, write the first five terms of each geometric sequence with the given first term and common ratio.

$a_{1} = - 4$ and $r = - 2$

Determine if each sequence is arithmetic. If so, indicate the common difference.

$(a) - 4, 4, 2, 10, 8, 16, \dots (b) - 3, - 1, 1, 3, 5, 7, \dots (c) 7, 2, - 3, - 8, - 13, - 18, \dots$

In the following exercises, expand each binomial.

$(s + t)^{7}$

Write the sum using summation notation: $1 + \frac{1}{4} + \frac{1}{9} + \frac{1}{16} + \frac{1}{25}$ .

See all solutions

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