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Chapter 7: Q. 9 (page 591)

Give a recursive definition for the sequence 1,2,3,4,....of positive integers. (Hint: Let a1=1.)

Short Answer

Expert verified

The recursive definition for the sequence1,2,3,4,.... isak=ak-1+1wherek≥2.

Step by step solution

01

Step 1. Given information

The given sequence is,

1,2,3,4,...of positive integers.

02

Step 2. We know that sequence of the consecutive positive integers with first term a1=1.

Now, the second term,

a2=2=1+1=a1+1

Hence, a2=a1+1.

Similarly, a3=a2+1.

Continuing, ak=ak-1+1.

Hence, the recursive definition for the sequence is,ak=ak-1+1wherek≥2.

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