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Chapter 12: Q 106. (page 1184)

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

The third term is 鈭�13 and the seventeenth term is 15.

Short Answer

Expert verified

The first term, common difference, and the general formula are -17, 2, andan=2n鈭�19.

Step by step solution

01

Step 1. Given Information.

The third term is 鈭�13 and the seventeenth term is 15.

02

Step 2. Write the equation for the third and seventeenth terms.

Use the arithmetic sequence formula as we have a3=鈭�13and a17=15.

a3=a1+3鈭�1d鈭�13=a1+2da1=鈭�13鈭�2d(1)

And,

role="math" localid="1645376363200" a17=a1+17鈭�1d15=a1+16da1=15鈭�16(2)

03

Step 3. Find the value of common difference d. 

Put equations 1 and 2 equal to find d.

鈭�13鈭�2d=15鈭�16d16d鈭�2d=15+1314d=28d=2

04

Step 4. Find the value of the first term.

Substitute 2 for d in equation 1.

a1=鈭�13鈭�22=-17

05

Step 5. Find the general term. 

Substitute -17 for the first term and 2 for d in the arithmetic formula.

a1=鈭�17+n鈭�12=鈭�17+2n鈭�2=2n鈭�19

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Most popular questions from this chapter

Find the twenty-seventh term of a sequence where the first term is 7 and the common difference is 9.

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

鈭�7,鈭�1,5,11,17,23,鈥�

Expand the partial sum and find its value:鈭�k=032k!

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�

Find the eleventh term of the sequence 7,14,28,56,112,224,鈥�Then find the general term for the sequence.
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