A young girl counts from 1 to 1000 using the fingers of her left hand as follows. She starts by calling her thumb 1, the first finger 2, middle finger 3, ring finger 4, and little finger 5. Then she reverses direction, calling the rung finger 6, middle finger 7, the first finger 8, and her thumb 9, after which she calls her first finger 10 and so on. If he continues to count in this manner, on which finger will she stop?

Use an expression for the arithmetic series.

Question

A young girl counts from 1 to 1000 using the fingers of her left hand as follows. She starts by calling her thumb 1, the first finger 2, middle finger 3, ring finger 4, and little finger 5. Then she reverses direction, calling the rung finger 6, middle finger 7, the first finger 8, and her thumb 9, after which she calls her first finger 10 and so on. If he continues to count in this manner, on which finger will she stop?

Use an expression for the arithmetic series.

calculusxy · Answer

@agent0smith @SolomonZelman @agent0smith @welshfella @ganeshie8

calculusxy · Answer

I have a_n = 8n + 1

solomonzelman · Answer

Well, after every 20, he returns to being thumb is 1.
Right?

calculusxy · Answer

I don't understand.

calculusxy · Answer

I am stuck with this because I know that 1000/8 = 125 but how can I use 8n+1 to support his?

calculusxy · Answer

Wait... does she land on the first finger?

solomonzelman · Answer

She starts from thumb = 1,
and ends at 10 = first finger.

(and does this over and over)

solomonzelman · Answer

If she counts till 1000, she simply does the same cycle 100 times, and stops at her first finger, because that completes the 100th cycle.

loser66 · Answer

|dw:1474936975594:dw|

calculusxy · Answer

Nevermind, my logic does not seem rational.

hughmungus14 · Answer

Hugh Mungus

loser66 · Answer

@calculusxy  need more explanation?

loser66 · Answer

|dw:1474937763487:dw|