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Chapter 12: Q 99. (page 1184)

Find the eighth term of a sequence where the seventh term is 鈭�8 and the common difference is 鈭�5. Give the formula for the general term.

Short Answer

Expert verified

The eighth term is -13 and the general term is an=鈭�5n+27.

Step by step solution

01

Step 1. Given Information. 

The seventh term is 鈭�8 and the common difference is 鈭�5.

02

Step 2. Find the first term by using the arithmetic formula. 

Substitute 7 for n, -5 for d, and the seventh term is -8, in the formula an=a1+n鈭�1d.

a7=a1+7鈭�1鈭�5鈭�8=a1鈭�30a1=22

03

Step 3. Find the eighth term.

Use the first term and the common difference to find the eighth term.

a8=22+8鈭�1鈭�5=22鈭�35=-13

04

Step 4. Find the general terms.

To find the general terms, substitute the first term 22 and the common difference -5 in the formula.

an=22+n鈭�1鈭�5=22鈭�5n+5=鈭�5n+27

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Most popular questions from this chapter

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

a1=64andr=14

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

(a)鈭�4,4,2,10,8,16,鈥�(b)鈭�3,鈭�1,1,3,5,7,鈥�(c)7,2,鈭�3,鈭�8,鈭�13,鈭�18,鈥�

In the following exercises, determine if each sequence is arithmetic, and if so, indicate the common difference.

1,2,4,8,16,32,鈥�

In the following exercises, evaluate.

(a) 81 (b) 1010 (c) 60 (d)93

In the following exercises, expand each binomial.

(a+b)6
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