Question

Help

Answer 1

???????

Answer 2

with

Answer 3

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

Answer 4

Okay so for number 4 the answer would be 25?

Answer 5

\(a_1=3\)
\(a_2=4\)
\(a_3=6\)
\(a_4=10\)
\(a_5=18\)
\(a_6=34\)
and so forth...

\(a_2=a_1+1\)
\(a_3=a_2+2=(a_1+1)+2=a_1+3=a_1+1+2\)
\(a_4=a_3+4=(a_1+3)+4=a_1+7=a_1-1+2(4)=a_1-1+2^{4-1}\)
\(a_5=a_4+8=(a_1+7)+8=a_1+15=a_1-1+2(8)=a_1-1+2^{5-1}\)
\(a_6=a_5+16=(a_1+15)+16=a_1+31=a_1-1+2(16)=a_1-1+2^{6-1}\)

\(a_n=a_1-1+2^{n-1}\)

Answer 6

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

Answer 7

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

Answer 8

And the number of marbles in any \(n\)th line is given by \(a_n\).

Answer 9

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

Answer 10

2+2\(^{7-1}\)
2+2\(^{6}\)
2+(2\(^{3}\))\(^2\)
2+8\(^2\)
2+64=66

this is a by-hand calculation.

Answer 11

okay so 66?

Answer 12

\(a_7\)=66

Answer 13

yes

Answer 14

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

Answer 15

yw