Anonymous
Anonymous asked in Science & MathematicsMathematics · 1 decade ago

# 5th grade math problem: if set 1 has 3 dots, set 2 has 6, and set 3 has 10, how many does set n=100 have?

my spouse came up with 5151 by counting *every* single set, but there HAS to be a formula.

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• 1 decade ago

S1 = 3

S2 = 3 + 3

S3 = 3 + 3 + 4

S4 = 3 + 3 + 4 + 5

...

Sn = 3 + 3 + 4 + 5 + ... + (n+1)

Sn = 3 + (3+n+1)*(n-1)/2

Sn = (6 + (n+4)*(n-1))/2

Sn = (n^2 + 3n + 2)/2

S100 = (100^2 + 3*100 + 2)/2

= (10000 + 302)/2

= 10302/2

= 5151

• Euro
Lv 4

Your spouse counted correctly. There is a simple formula.

It is ((n+1)*(n+2))/2

so for 100 it is

(101*102)/2 = 10 302/2 = 5151

• 1 decade ago

s(1) = 1+2

s(2) = 1+2+3

s(3) = 1+2+3+4

.

.

s(n) = (n+1)(n+2)/2

s(100) = 101 * 102 / 2 = 5151

• 1 decade ago

the differences grow by a fixed amount - so this is a quadratic sequence with a general formula t(n)=an^2+bn+c

t(1)=3=a+b+c

t(2)=6=4a+2b+c

t(3)=10=9a+3b+c

t(3)-t(2)=5a+b=4

t(2)-t(1)=3a+b=3

t(3)-2t(2)+t(1)=2a=1

a=0.5

t(3)-t(2)=5*0.5+b=4

b=4-2.5=1.5

t(1)=0.5+1.5+c=3

c=3-2=1

so the specific formula is:

t(n)=0.5n^2+1.5n+1

and

t(100)=5000+150+1=5151

• Anonymous

Yeh Dj is right.

There's no formula to this because there is no connection between (sets 1 & 2) and (set 3). I would not classify this as 5th grade math unless set 3 equalled 9 dots.