A little girl counts using the fingers of her left hand as follows: She starts by calling her thumb 1, the first finger 2, middle finder 3, ring finger 4, and little finger 5. Then she reverses direction, calling the ring finger 6, middle finger 7, first finger 8 and thumb 9, after which she calls her first finger 10 and so on. If she continues to count in this manner, on which finger will she stop? a) What if the girl counts from 1 to 10?
b) What if the girl counts from 1 to 100?
c) What if the girl counts from 1 to 1000?

(a) Index finger

(b) Ring finger

(c) Index finger

Step-by-step explanation:

Taking thumb as standard for the question.

Thumb series 1 , 9 , 17 ,25, 33

general term for this

a(n) = 1 + (n-1)8

      = 1 + 8n -8

       = 8n -7

(a) For 1 to 10

     8n -7 = 10

     8n = 16+1 (remainder)

so the thumb is for 9 and the next is index finger.

10th = index finger.

(b) for 1 to 100

    8n - 7 = 100

      8n= 107

     107 = 13x 8 + 3(remainder)

so the third finger from thumb is Ring finger

100th = Ring finger

(c) 8n - 7 = 1000

   8n = 1007      

 1007= 125x8 +7 (remainder)

so the 7th finger next to thumb is Index finger

1000th = index finger

δabc ≅ δdcb by sas because

db ≅ ac . . given (side)

bc ≅ bc . . reflexive property (side)

∠dbc ≅ ∠ acb . . alternate interior angles where transversal bc crosses parallel lines bd and ac (included angle)