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Chapter 12: Q 105. (page 1184)

Find the first term and common difference of the sequence with the given terms. Give the formula for the general term.

The fourth term is 鈭�6 and the fifteenth term is 27.

Short Answer

Expert verified

The first term, common difference, and the general formula are -15, 3, andan=3n鈭�18.

Step by step solution

01

Step 1. Given Information.

The fourth term is 鈭�6 and the fifteenth term is 27.

02

Step 2. Write the equation for the second and tenth terms.

Use the arithmetic sequence formula as we have a4=鈭�6and a15=27.

role="math" localid="1645374037302" a4=a1+4鈭�1d鈭�6=a1+3da1=鈭�6鈭�3d(1)

And,

role="math" localid="1645374162245" a15=a1+15鈭�1d27=a1+14da1=27鈭�14d(2)

03

Step 3. Find the value of common difference d.

Put equations 1 and 2 equal to findd.

鈭�6鈭�3d=27鈭�14d14d鈭�3d=27+611d=33d=3

04

Step 4. Find the value of the first term.

Substitute 3 for d in equation 1.

a1=鈭�6鈭�33=-15

05

Step 5. Find the general term.

Substitute -15 for the first term and 3 for d in the arithmetic formula.

an=鈭�15+n鈭�13=鈭�15+3n鈭�3=3n鈭�18

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