Question

Consider Akelia’s sequence 5, 8, 11, 14, 17, …. b. Write a formula for Akelia’s sequence

Answer 1

Answer:

A(n+1)=A(n)+3, for n>=0 and A(1)=5

Step-by-step explanation:

This sequence can be expressed in a recursive form. A recursive formula is one where each term can be expressed as a function of its preceding terms. For example; term 5 precedes 8, 8 precedes 11, 11 precedes 14, and 14 precedes 17.

The terms can be expressed as follows;

A(n+1)=A(n)+3, for n>=0 and A(1)=5

where;

A(1): First term

n: nth term

A(n): current term

A(n+1): Next term

d=3: common difference

Since in order to get the next term, one has to add 3 to the preceding term, therefor 3 is the common difference between A(n+1) and A(n)+3

Therefor;

A(n+1)=A(n)+3, for n>=0 and A(1)=5