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Chapter 12: Q 12.32. (page 1179)

Find the nineteenth term of a sequence where the fifth term is 1 and the common difference is 鈭�4. Give the formula for the general term.

Short Answer

Expert verified

The nineteenth term is -55 and the general term is an=21鈭�4n.

Step by step solution

01

Step 1. Given Information.

The fifth term is 1 and the common difference is 鈭�4.

02

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

Substitute 5 for n,-4 for d, and the fifth term is 1, in the formula an=a1+n鈭�1d.

a5=a1+5鈭�1鈭�41=a1鈭�16a1=17

03

Step 3. Find the eleventh term. 

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

a19=17+19鈭�1鈭�4=17-72=-55

04

Step 4. Find the general terms. 

To find the general terms, substitute the first term 17 and the common difference -4 in the formula.

an=17+n鈭�1鈭�4=17鈭�4n+4=21鈭�4n

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Most popular questions from this chapter

Write the first five terms of the sequence whose general term is an=n!(n+1)!.

Write the first five terms of the sequence where the first term is 7 and the common ratio is r=-3.

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�

Write each sum using summation notation: 1 鈭� 4 + 9 鈭� 16 + 25.

Find a general term for the sequence whose first five terms are shown. 4, 8, 12, 16, 20, 鈥�
See all solutions

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