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Chapter 11: Q45. (page 582)

Complete the statement for each arithmetic sequence.

-14 is the ___?__ term of 215,2,145,....

Short Answer

Expert verified

-14 is the82nd termof the arithmetic sequence 215,2,145,....

Step by step solution

01

Step 1. Given Information.

Given arithmetic sequence is 215,2,145,...

02

Step 2. Calculation.

The nth term of an arithmetic sequence is given by an=a1+(n鈭�1)d.

Here the first term is a1=215

The difference between the first two terms is 2鈭�215=鈭�15

The difference between the second two terms is 145鈭�2=鈭�15

The common difference is d=鈭�15

The given nth term is an=鈭�14

Plugging the values in the formula:

an=a1+(n鈭�1)d鈭�14=215+(n鈭�1)(鈭�15)鈭�14鈭�215=(n鈭�1)(鈭�15)(n鈭�1)(鈭�15)=鈭�815n鈭�1=81n=81+1n=82

03

Step 3. Conclusion.

Hence, -14 is the 82nd term of the arithmetic sequence 215,2,145,....

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