Question

Tell whether the sequence is arithmetic. Justify your answer. If the sequence is arithmetic, write a recursive
formula and an explicit formula to represent it.

3, 3.25, 3.5, 3.75,...
​

Answer 1

Answer:

The explicit formula

$a_n = 3 +0.25 (n-1)$

The recursive formula

$a_1 = 3$                            for $n=1$

$a_n = a_ {(n-1)} +0.25$     if $n>1$

Step-by-step explanation:

If a sequence is arithmetical then the difference between any of its consecutive terms will be constant

3, 3.25, 3.5, 3.75,

$3.25-3 = 0.25\\\\3.5-3.25 = 0.25\\\\3.75 -3.5 = 0.25$

The difference between the consecutive terms remains constant so the sequence is arithmetic.

The explicit formula for an arithmetic sequence is:

$a_n = a_1 + d (n-1)$

Where d is the constant difference between the terms.

$d = 0.25$

$a_1$ is the first term of the sequence.

$a_1 = 3$

So

$a_n = 3 +0.25 (n-1)$

Finally, the recursive formula is:

$a_1 = 3\\\\a_n = a_ {(n-1)} +0.25$