Write the recursive formula for 5, 15, 30, 50, .........
To write the recursive formula for the given sequence 5, 15, 30, 50, ...... , we need to identify the pattern and the rule that generates each term.
We can observe that each term in the sequence is obtained by adding a specific number, which increases with each term, to the previous term. Specifically, to get from one term to the next, we add 10, 15, 20, and so on.
Therefore, we can write the recursive formula as:
a1 = 5 (the first term is 5)
an = an-1 + 10n -5 (for n > 1)
This formula states that any term in the sequence (other than the first) is obtained by adding the term before it to (10n - 5), where n is the position of the term in the sequence.