Question

Online Homework Generating sequences Russian International School Matvey Mihailuk Save = Menu 000 Q1 Q2 - nth term rules The nth term of a sequence is 3(n + 4). 0 What are the first four terms? 15 18 21 24 [4] What is the 50th term? Q2 [2] 0 Which is the first term to be larger than 100? The th term [2] 18 The nth term of a sequence is n(n + 1). No calc What are the first four terms? , D.O.O [4] What is the 20th term? [2] Is 51 a term in the sequence? yes no Total [2] 0 Which term is 210? The th term [2] 30 Mark it

Answer 1

what a heck is that?!?.………

Answer 2

It seems like you have a series of questions related to generating sequences. I'll do my best to answer each question in detail.

Question 1: What are the first four terms of the sequence given by the nth term rule 3(n + 4)?

To find the first four terms of the sequence, we substitute the values of n starting from 0 up to 3 into the nth term rule.

When n = 0: 3(0 + 4) = 3(4) = 12

When n = 1: 3(1 + 4) = 3(5) = 15

When n = 2: 3(2 + 4) = 3(6) = 18

When n = 3: 3(3 + 4) = 3(7) = 21

Therefore, the first four terms of the sequence are 12, 15, 18, and 21.

Question 2: What is the 50th term of the sequence?

To find the 50th term of the sequence, we substitute n = 49 into the nth term rule.

3(49 + 4) = 3(53) = 159

Therefore, the 50th term of the sequence is 159.

Question 3: Which is the first term to be larger than 100?

To find the first term that is larger than 100, we need to find the smallest value of n that satisfies the inequality 3(n + 4) > 100.

3(n + 4) > 100 3n + 12 > 100 3n > 100 - 12 3n > 88 n > 88 / 3 n > 29.33

The smallest integer value of n that satisfies the inequality is 30. Therefore, the first term to be larger than 100 is when n = 30.

Question 4: What are the first four terms of the sequence given by the nth term rule n(n + 1), without using a calculator?

To find the first four terms of the sequence, we substitute the values of n starting from 0 up to 3 into the nth term rule.

When n = 0: 0(0 + 1) = 0

When n = 1: 1(1 + 1) = 2

When n = 2: 2(2 + 1) = 6

When n = 3: 3(3 + 1) = 12

Therefore, the first four terms of the sequence are 0, 2, 6, and 12.

Question 5: What is the 20th term of the sequence?

To find the 20th term of the sequence, we substitute n = 19 into the nth term rule.

19(19 + 1) = 19(20) = 380

Therefore, the 20th term of the sequence is 380.

Question 6: Is 51 a term in the sequence?

To determine if 51 is a term in the sequence, we substitute n = 8 into the nth term rule.

8(8 + 1) = 8(9) = 72

Since 51 is not equal to 72, it is not a term in the sequence.

Question 7: Which term is 210 in the sequence?

To find which term is equal to 210, we need to solve the equation 210 = n(n + 1) for n.

n(n + 1) = 210 n^2 + n - 210 = 0

Using factoring or the quadratic formula, we find that n = 14 or n = -15. However, n cannot be negative in this context, so the term that is equal to 210 is the 14th term.

Mark it

I'm sorry, but I'm not sure what you mean by "Mark it." Could you please provide more context or clarify your question?