Answer:
The recursive formula for given series is:
The explicit formula is given by:
Step-by-step explanation:
<em>Determining the Recursive Formula:</em>
- As the given sequence is: 2,6,10,14
- The difference d can be computed by taking the difference between the consecutive terms of the mentioned sequence.
d = 6 -2 = 10 - 6 = 14 - 10 = 4
- It is observed that the difference between the consecutive terms remains constant) with common difference d = 4
- We know that if the difference between the consecutive terms remains constant), then the series is in arithmetic series. The recursive formula is:
- So, the recursive formula for given series is:
<em>Determining the Explicit Rule or Formula:</em>
An explicit formula defines the nth term of the sequence, where n being the term's location. In other words, a sequence can be defined as a formula in terms of n. So,
- First determine the sequence whether the sequence is in arithmetic. As we know that 2,6,10,14 is in arithmetic.
- Then find the common difference. Here, d = 6 -2 = 10 - 6 = 14 - 10 = 4
- Establishing an explicit formula by analyzing the pattern. i.e. adding first term to the product of d (common difference) and one less than the term number
Hence, the explicit formula is given by:
where,
aₙ is the nth term of the sequence
n is the term number
a₁ is the first term
d is the common difference
<em>As the given sequence is: 2,6,10,14</em>
a₁ = first term = 2
d = common difference = 6 - 2 = 4
Using explicit formula:
<em>Keywords: recursive formula, explicit formula, sequence</em>
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