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Chapter 7: Q. 29 (page 592)

In Exercises, find a plausible formula for the general term of the given sequence.

23,35,47,59,鈥�

Short Answer

Expert verified

The plausible formula for the general term of the sequence isak=k+12k+1wherek鈮�1.

Step by step solution

01

Step 1. Given information.

The given sequence is23,35,47,59,鈥�.

02

Step 2. plausible formula for the general term. 

write the sequence in a pattern.

23,35,47,59,鈥�=1+12(1)+1,2+12(2)+1,3+12(3)+1,4+12(4)+1,鈥�23,35,47,59,鈥�=k+12k+1k=1鈭�

for every term, the numerator is k+1and the denominator is 2k+1andlocalid="1649189107593" k鈮�1.

So plausible formula for the general term of the sequence islocalid="1649189440639" ak=k+12k+1.

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