Question

A group of students is arranging squares into layers to create a project. The first layer has 5 squares. The second layer has 10 squares. Which formula represents arithmetic explicit formula to determine the number of squares in each layer?
A.a1 = 5; an = 5 ⋅ an − 1, n > 0
B.a1 = 5; an = 5 ⋅ an + 1, n > 0
C.a1 = 5; an = 5 + an − 1, n > 0
D.a1 = 5; an = 5 + an + 1, n > 0

Answer 1

Answer:

• Recursive formula:

                                         $a_1=5;a_n=5+a_{n-1},n>0$

Explanation:

All the shown formulae in the choice list are recursive formulae instead of explicit formulae.

Explicit formulae that represent arithmetic sequences are of the form:

• $a_n=a_1+(d-1)n$

That kind of formula permits to determine any term knowing the first term, the number of the term searched, and the common difference (d).

On the other hand, the recursive formulae let you to calculate one term knowing the previous term and the difference.

In this case, the difference in the number of squares of two consecutive terms is:

• differece = number of squares in the second layer - number of squares in the first layer.

• d = 10 - 5 = 5

Then, the recursive formula is:

• $a_1=5;a_n=5+a_{n-1},n>0$