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anonymous · Answer

???????

anonymous · Answer

with

zarkam21 · Answer

attachment

solomonzelman · Answer

So, first you add 1.
Then, you add 2.
Then, add 4.

zarkam21 · Answer

Okay so for number 4 the answer would be 25?

solomonzelman · Answer

$a_1=3$
$a_2=4$
$a_3=6$
$a_4=10$
$a_5=18$
$a_6=34$
and so forth...

$a_2=a_1+1$
$a_3=a_2+2=(a_1+1)+2=a_1+3=a_1+1+2$
$a_4=a_3+4=(a_1+3)+4=a_1+7=a_1-1+2(4)=a_1-1+2^{4-1}$
$a_5=a_4+8=(a_1+7)+8=a_1+15=a_1-1+2(8)=a_1-1+2^{5-1}$
$a_6=a_5+16=(a_1+15)+16=a_1+31=a_1-1+2(16)=a_1-1+2^{6-1}$

$a_n=a_1-1+2^{n-1}$

solomonzelman · Answer

I played around a little bit, and derived the following formula for the sequence, just in case you need it.

solomonzelman · Answer

and you can further simplify this, knowing that $a_1=3$
$a_n=2+2^{n-1}$

solomonzelman · Answer

And the number of marbles in any $n$th line is given by $a_n$.

zarkam21 · Answer

So for the 7th line, there will be 50?

solomonzelman · Answer

2+2$^{7-1}$
2+2$^{6}$
2+(2$^{3}$)$^2$
2+8$^2$
2+64=66

this is a by-hand calculation.

zarkam21 · Answer

okay so 66?

solomonzelman · Answer

$a_7$=66

solomonzelman · Answer

yes

zarkam21 · Answer

Oh okay I understand the pattern now,, thanks ! :]

solomonzelman · Answer

yw