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klasskru [66]
3 years ago
14

PLEASE HELP!!!!! 3, 8, 13, 18, 23, .... The recursive formula for this sequence is:

Mathematics
1 answer:
rodikova [14]3 years ago
8 0

Answer:

a₈ = 37

Step-by-step explanation:

The given arithmetic sequence is: 3, 8, 13, 18, 23, . . .

The recursive formula for the sequence is: $ a_n = a_{n - 1} + 5 $

Here, $ a_n $ represents the $ n^{th} $ of the sequence.

And, $ a_{n - 1} $ represents the $ (n - 1)^{th} $ of the sequence.

'+5' denotes that '5' is added to the $ (n - 1)^{th} $ term to get the $ n^{th} $ term. In other words, the difference between two consecutive numbers in the sequence is 5.

Now, we are asked to find a₈ i.e., n =8.

Substituting in the recursive formula we get: a₈ = a₍₈₋ ₁₎ + 5 = a₇ + 5.

So, to determine a₈ we need to know a₇. From the sequence we see that a₅ = 23.

⇒ a₆ = 23 + 5 = 28.

⇒ a₇ = 28 + 5 = 32.

⇒ a₈ = 32 + 5 = 37.

Therefore, the $ 8^{th} $ term of the sequence is 37.

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