A sequence is defined by a_n = n^2 when n is not divisible by 3, and a…

Question

A sequence is defined by a_n = n^2 when n is not divisible by 3, and a_n = n/3 when n is divisible by 3. What are its first six terms?

Accepted Answer

B. {1, 4, 1, 16, 25, 2}

1. For a piecewise formula, first decide which branch each value of n falls into.
2. n = 1, 2, 4 and 5 are not multiples of 3, so use n^2: the values are 1, 4, 16 and 25.
3. n = 3 and n = 6 are multiples of 3, so use n/3: the values are 1 and 2.
4. Assembling them in order gives {1, 4, 1, 16, 25, 2}.
5. Applying n^2 throughout would give 36 at the sixth position, which is the trap in the option ending in 36.
_Source: OpenStax Algebra and Trigonometry (CC BY 4.0), Ch 13 "Sequences, Probability and Counting Theory", section 13.1 Sequences and Their Notations_

Answer

{1, 4, 9, 16, 25, 36}

Answer

{1, 4, 1, 16, 25, 36}

Answer

{1, 2, 1, 16, 5, 2}

A sequence is defined by a_n = n^2 when n is not divisible by 3, and a_n = n/3 when n is divisible by 3. What are its first six terms?

Keep practising Sequences, Probability and Counting Theory