Question

Select the function that represents an arithmetic sequence.

a.a(n) = p(1 + i)n – 1, where n is a positive integer
b.a(n) = p + (n – 1)i • p, where n is any real number
c.a(n) = p + (n – 1)i • p, where n is a positive integer
d.a(n) = p(1 + i)n – 1, where n is any real number

Answer 1

Because n must be a positive integer we can eliminate b and d. Assume i=√-1.
Of the two remaining options, c has the correct format for an AP with constant difference ip.

Answer 2

Option C is correct.

Explanation:

We have to select which function represent an Arithmetic Sequence.

nth term of AP is equal to a + ( n - 1 ) d

We know that in Arithmetic Sequence value of n is natural number or say a positive number.

So, Option B and D are rejected.

Now in Option A

a(n) = p (1 + i )n - 1 = ( p + pi )n - 1 = pn +ipn - 1

putting value of i = √-1, we get

a(n) = pn + √-1 pn - 1 = ( 1 + √-1 ) np - 1

but this does not represent the nth term of AP.

Now in Option C

a(n) = p + (n - 1)i×p

This represent the nth term of AP with first term, a = p and common difference, d = ip

Therefore, Option C is correct.