The first 12 terms of the fibonacci sequence are:1,1,2,3,5,8,13,21,34,55,89,144.

Question

Look for a pattern in the following information that will allow you to predict answer to 1+1+2+3+5+...+144.

1+1=  3-1 = 2

 

1+1+2=  5-1 =4

 

1+1+2+3=  8-1 =7

 

1+1+2+3+5=  13-1 =12

Answer 1

Each sum is the second term after minus one.

 

The fist term after 144 is 89 + 144 = 233

The second term after 144 is 144 + 233 = 377

 

The sum of the first 12 terms is 377 - 1 = 376

Answer 2

The Fibonacci Sequence is important in math.  Have fun learning all about it !
 
Let’s list the sequence with the sum so far beneath each number:

1        1         2        3        5         8        13      21      34     55      89     144    233     377
          2         4        7       12       20       33      54      88    143    232     376                   

 Now, just for fun, let’s slide the bottom row to the right two places
   And subtract like they did in the problem:

1        1        2       3       5        8       13      21      34     55     89      144      233      377
                            2        4        7       12      20      33     54     88      143     232      376
                            1        1        1         1        1       1       1       1          1        1          1

This is great !  The sum of the Fibonacci Sequence up to 144 is 376, which is the Fibonacci two places past 144 (that is, 377) then minus 1.

Answer 3

Find out whatever the term is after 144, and do 144 plus that number -1 to complete the pattern.