Math  /  Discrete

QuestionThe sequence below is the start of the triangular number sequence. Work out the next two number terms in the sequence.

Studdy Solution

STEP 1

What is this asking? We need to find the next two numbers in the triangular number sequence, where each number represents the total number of dots arranged in an ever-growing triangle! Watch out! Don't just add the same number each time; the difference between the numbers *itself* is increasing!

STEP 2

1. Understand the Pattern
2. Calculate the Next Term
3. Calculate the Term After That

STEP 3

Alright, let's look closely at how this sequence grows!
We start with 11 dot.
Then, we add 22 dots to get 33.
Next, we add 33 dots to get 66.
See the pattern?
Each time, we're adding one more dot than we did before!

STEP 4

So, from 11 to 33, we add 22.
From 33 to 66, we add 33.
From 66 to 1010, we add 44.
This means the differences between the numbers are increasing by 11 each time.
This is super important!

STEP 5

Following the pattern, to get the next number after 1010, we need to add 55 (since we added 44 to get to 1010).

STEP 6

So, 10+5=1510 + 5 = \textbf{15}.
The next term in the sequence is **15**!
Awesome!

STEP 7

Now, we need to find the term *after* 1515.
Since we added 55 to get to 1515, we now need to add 66 to 1515.

STEP 8

15+6=2115 + 6 = \textbf{21}.
So, the next term after 1515 is **21**!
Boom!

STEP 9

The next two terms in the sequence are **15** and **21**!

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