How Many Dots Come Next?

There triangles follow a pattern of adding successive numbers.

$1^{st}$ triangle $= 1$ dot.
$2^{nd}$ triangle $= 1 + 2 = 3$ dots.
$3^{rd}$ triangle $= 1 + 2 + 3 = 6$ dots.
$4^{th}$ triangle $= 1 + 2 + 3 +4 = 10$ dots.
$5^{th}$ triangle $= 1 + 2 + 3 + 4 + 5 = 15$ dots.

So, the number triangle will contain $\boxed{15}$ dots.

Use the formula $\frac{n(n+1)}{2}$

Substitute n=5, we can get $\boxed{15}$

I found an another solution to this. The number of dots on each side is increasing by 1.

Assume a figure to be a rectangle of side 4

Pic: Dots1 Total number of circles: 4*4 = 16

Now, Divide it in half Pic: Dots2 Total number of circles : 16/2 = 8

But circles in center line got halved as well Pic: Dots3

Adding those half circles: Total circles in diagonal = circles in each side = 4 Half of it = 2

Add it to total circles: 8 + 2 = 10

Deducing a formula: total circles = (s*s) / 2 + s/2 i.e. s(s + 1 ) / 2 where s is total number of cicles in one side.

OMG if you noticed something this is the formula for calculation 4 + 3 + 2 + 1. :D

We notice that we keep on adding successive numbers to the previous figure to get the number of dots in the next figure. For example, we add $2$ dots to get from figure $1$ to figure $2$ . We add $3$ dots to get from figure $2$ to figure $3$ . We add $4$ dots to get from figure $3$ to figure $4$ ; thus, we need to add $5$ dots to get to figure $5$ , so our answer is $10+5=\boxed{15}$ .

Addition of successive numbers will give 15 for the next sequence

just add successive numbers

These are triangular numbers nth triangular number is = n(n+1)/2 here n = 5 so number is 5 × 6/2 = 15

Because it increases by 1,2,3,4 and the next is 5

There triangles follow a pattern of adding successive numbers.

triangle one dot

triangle three dots

triangle six dots

triangle ten dots

triangle fifteen dots

So, the number triangle will contain dots.

Consider this recursion and solve the problem: $F_{n} = F_{n-1} + n$ , where $F_{1} = 1$ and $F_{2} = 3$ We get $F_{5} = 10 + 5 = 15$

Did anyone else just count the dots?

the difference between any two goes in a (+1) sequence.

With each nth triangle add n+1.

instead of looking at the dots see the series below 1,3,6,10,? it starts with 2 the nunber gets increased by 1

ans.15

From observation of all triangles , the triangle next to the other triangle has the dots of the base incresed by one . Let the base dots be n , then total no of dots of triangle is said by the sumof n-1,n-2,n-3, _ _n-n+1

first was 1 second was 3, third was 6' fourth was 10, it means each time we added one more than previous time like second time we added 2 and we had then 3 than after 3 we added 2+1=3 so we receive 3+3=6 then we added 3+1=4 so we receive 6+4=10 so after 10 we would have 4+1=5 so 10 +5=15

Count the difference of subsequent stages. You will get the answer.

Just we have to see that how much the dot are
greater than the previous pattern . For example second pattern has two more dots than first pattern and third pattern has three more dots than second pattern and fourth pattern has four more dots than third pattern . So fifth must have five more dots than fourth pattern ,
therefore the answer must be 15.

Write a solution.

We have to find the 5th one of the series . So we'll get that simply by adding 5 to the previous no. which in this case is 10+5=15 !

n (n+2) / 2

Simple formula is used, n(n+1)/2 where n is no. of triangles.

1=1, 1+2=3, 1+2+3=6, 1+2+3+4=10, 1+2+3+4+5=15. ans=15

We can use either 1, 1+2, 1+2+3... pattern or by simply looking just add 5 to 10 since it started with 1 then by adding 2 into it to get 3 then add 3 to get 6 add 4 to get 10 and finally add 5 to 10 get 15.

The 1st triangle here is of one dot
Next one = 1+2
3rd triangle = 1+2+3
4th triangle = 1+2+3+4
5th triangle = 1+2+3+4+5 = 15 dots

By looking at the base of the triangle, you can solve it much faster than anyone else ..........

The formula is $\frac{n(n+1)}{2}$ to find the number of dots in the $nth$ figure. We plug in $5$ and get $\boxed{15}$ .

2nd triangle increased by 2 dots from 1st , 3rd triangle increased by 3 dots from 2nd , 4th triangle increased by 4 dots from 3rd, therefore 5th dot will increase by 5 dots from 4th

Differences of differences of given numbers form an arithmetic progression with common difference 1.

addition of 1dot in each coming triangle with addition of each row... 1, 3, 6. 10, 15... difference of 2,3,4,...................... so in series next digit will be {5}

my solution is , the 1 to 3 interval is 1 then the second set's interval is 2 then the third interval is 4 and the fourth will be 5that's why it's 15... do you get it? me too i dont ahaha :D

1+2+3+4+5=15 dots

1=1, 1+2=3, 1+2+3=6 ,1+2+3+4=10, 1+2+3+4+5=15

My solution Difference between first and second is 2 Difference between second and third is 3 and between third and fourth is 4 so difference is increasing as 1,2,3,4. So next triangle should be 10+5

5+4+3+2+1=15

sum of first n natural number....since we have to find out number of dots in 5th triangle .... number of dots is 5(5+1)/2 = 15.(using Sn = n(n+1)/2 )

120

It is a methemstical series n /2 (1 + n)

triangulo(n) = triangulo(n-1) + n

It is Fibonacci Sequence. next in sequence is number 21

Tn1=1 (n=1) Tn2=3 (n=2) Tn3=6 (n=3) Tn4=10 (n=4) Tn5=15 (n=5) ...

(n^2)-Tn-1

0+1=1, 1+2=3, 3+3=6, 6+4=10, 10+5 ; Just add the increment by 1 of previously addedd with previous outcome.

It is simple arithmetic series situation. nth term will be nx(n+1)/2 =15.

0 + 1 + 2 + 3 + 4 + 5 =15 . Easy

Given tringle that 1st tringle = 1 dot, 2nd tringle = 1+ 2=3dots 3rd tringle = 3+ 3=6 dots 4th tringle = 6+ 4=10 dots so same going on 5th Tringle=10+ 5=15 dots so last tringle has 15 dots

This problem number of dots increases as triangle so in 1'st 1dot , in second (1+2=3) dots ; in 3'rd (1+2+3=6) dots ; in 4'th (1+2+3+4=10) dots then in 5'th (1+2+3+4+5=15) dots.

Triangle 1= 1 dot

Triangle 2= 1 dot + 2 dots = 3 dots

Triangle 3= 3 dots + 3 dots =6 dots

Triangle 4= 6 dots + 4 dots= 10 dots

You maintain the patter of adding one number higher each time. So the next number after 4 is 5 so

Triangle 5= 10 dots + 5 dots = 15 dots

Triangle 1st = 1 dot

Triangle 2nd = 1 + 2 = 3 dots

Triangle 3rd = 3 + 3 = 6 dots

Triangle 4th = 6 + 4 = 10 dots

Here we see that 1 no. is added in every next triangle. Thus next will be

Triangle 5th = 10 + 5 = 15 dots

similarly next will be

Triangle 6th = 15 + 6 = 21 dots

Triangle 7th = 21 + 7 = 28 dots