Question

The nth term of the sequence is n^2 + 20

Answer 1

Answer: 5 terms.

Step-by-step explanation:

We know that the n-th term of a sequence is:

Aₙ = n² + 20

Where n can be any natural number, then n ∈ {1, 2, 3, ...}

We want to find how many terms are smaller than 50.

Then we could find the first value of n such that Aₙ is equal or larger than 50.

Then we can solve:

Aₙ = n² + 20 = 50

then:

n² = 50 - 20 = 30

n = √30 = 5.48

This is not a natural number, so we need to round to the next one that is n = 6

This means that the first natural number n such that Aₙ is equal or larger than 50 is n = 6, then for the values:

n = 1, 2, 3, 4, 5

Aₙ is smaller than 50

This means that there are 5 terms of the sequence that are smaller than 50.