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Chapter 12: Q 95. (page 1184)

Find the twentieth term of a sequence where the fifth term is 鈭�4 and the common difference is 鈭�2. Give the formula for the general term.

Short Answer

Expert verified

The twentieth term is -34 and the general term isan=鈭�2n+6

Step by step solution

01

Step 1. Given Informaation. 

The fifth term is 鈭�4 and the common difference is 鈭�2.

02

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

Substitute 5 for n,-2 for d, and the fifth term is -4, in the formula an=a1+n鈭�1d.

a5=a1+5鈭�1鈭�2鈭�4=a1鈭�8a1=4

03

Step 3. Find the twentieth term.

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

a20=4+20鈭�1鈭�2=4鈭�38=-34

04

Step 4. Find the general terms.

To find the general terms, substitute the first term 4 and the common difference -2 in the formula.

an=4+n鈭�1鈭�2=4鈭�2n+2=鈭�2n+6

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