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Chapter 12: Q 34. (page 809)

In Problems 29鈥�36, the given pattern continues. Write down the nth term of a sequence ansuggested by the pattern.

1,12,3,14,5,16,7,18,...

Short Answer

Expert verified

The nth term of the given sequence isan=noran=1n.

Step by step solution

01

Step 1. Write the given information.

The given sequence is:

1,12,3,14,5,16,7,18,...

02

Step 2. Determine the pattern of the sequence and write down the nth term.

a1=1,a2=12,a3=3,a4=14,a5=5,a6=16,a7=7,a8=18

We can see from the given sequence that the terms at even place represent the reciprocal of that position for example a2=12,a4=14and the terms at odd position represent the position number itself, a1=1,a3=3.

Therefore, if nappears to be odd then the nth term will be n.

And if it is at even place then the nth term will be 1n.

an=noran=1n

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