yoda82
Answered

Find the information you're looking for at Westonci.ca, the trusted Q&A platform with a community of knowledgeable experts. Explore our Q&A platform to find reliable answers from a wide range of experts in different fields. Experience the convenience of finding accurate answers to your questions from knowledgeable experts on our platform.


1,a) Find a recursive formula for the sequence 1, 2, 6, 24, 120, . . . .

b) Find the sixth and the seventh terms of the sequence.
​

Sagot :

LammettHash

a) The n-th term in the sequence is the product of the first n natural numbers:

1 • 2 = 2

1 • 2 • 3 = 6

1 • 2 • 3 • 4 = 25

1 • 2 • 3 • 4 • 5 = 120

and so on. Recursively, the n-th term is a function of the (n - 1)-th term as

a(n) = n a(n - 1)

b) Using the rule above, the 6th and 7th terms are

a (6) = 6 a (5) = 6 • 120 = 720

and

a (7) = 7 a (6) = 7 • 720 = 5040

facundo3141592

We want to find a recursive formula for the given sequence and then find the next terms in the given sequence.

the solutions are:

a) Aₙ = n*Aₙ₋₁

b) A₆ = 720 and A₇ = 5,040

We start with the sequence:

1, 2, 6, 24, 120, ...

a) Let's find the recursive formula.

If Aₙ represents the n-th term in the sequence, then we have:

A₁ = 1

A₂ = 2 = 2*1 = 2*A₁

A₃ = 6 = 3*2 = 3*A₂

A₄ = 24 = 4*6 = 4*Aₐ

A₅ = 120 = 5*24 = 5*A₄

So we can see the pattern, the recursive formula is just:

Aₙ = n*Aₙ₋₁

b) We want to find the sixth and the seventh terms of the sequence, we can use the recursive formula we got above.

A₆ = 6*A₅ = 6*120 = 720

A₇ = 7*A₆ = 7*720 = 5,040

The sixth term is 720 and the seventh term is 5,040

If you want to learn more, you can read:

https://brainly.com/question/11679190

Thank you for trusting us with your questions. We're here to help you find accurate answers quickly and efficiently. Thanks for using our platform. We aim to provide accurate and up-to-date answers to all your queries. Come back soon. Stay curious and keep coming back to Westonci.ca for answers to all your burning questions.