Question

The Fibonacci sequence is the sequence 1, 1, 2, 3, 5, ... where the first and second terms are 1 and each term after that is the sum of the previous two terms. What is the remainder when the 100th term of the sequence is divided by 8?

Answer 1

Answer:

44,278,106,022,432,739,384.375  =   1/8 of ((1+√5)/2)^100/√5

Step-by-step explanation:

We separate the x10^21 number into 2 so that becomes x10^8 number with decimal of .75 when it is a x10^21 split into 2 large parts and a small subtraction creates the third step. we have found 1/4 then we half.

354224848179261915075 / 4

= 000000000000065478768.75

354224  848179000000000/4

-88556212044.8

= 354 has become a 12 digit number temporary starting with 885 the decimal .8 is simply put in front

3542248481  79-  so it has become a x10^20 number. 885562120448,65478768.75

We arrange the comma's

  88,556,212,044,865,478,768.75

  88,556,212,044,865,478,768.75

  88,556,212,044,865,478,768.75

  88,556,212,044,865,478,768.75  is division by 4

=354224848179261915075

88,556,212,044,865,478,768.75 /2

= 44278106022 (/2) 432739384.375(/2)  in two part.

=  44278106022,432739384.375 replace /2 with comma

= 44,278,106,022,432,739,384.375 replace all other comma.