SOLUTION: make a conjecture about the number of squares in the nth sketch: pattern1: 3 squares, pattern 2: 5 squares,pattern 3:7 squares and so fourth MY ANSWER? I CAN CONJECTURE THAT IF T

Algebra ->  Sequences-and-series -> SOLUTION: make a conjecture about the number of squares in the nth sketch: pattern1: 3 squares, pattern 2: 5 squares,pattern 3:7 squares and so fourth MY ANSWER? I CAN CONJECTURE THAT IF T      Log On


   

Question 1067945: make a conjecture about the number of squares in the nth sketch:
pattern1: 3 squares, pattern 2: 5 squares,pattern 3:7 squares and so fourth
MY ANSWER? I CAN CONJECTURE THAT IF THE PATTERN CONTINUES YOU CAN ADD 2 TO THE PREVIOUS COUNTING NUMBER TO GET THE NEXT TERM. is this right?
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
your conjecture is correct, but that doesn't tell you how many squares are in the nth sketch.

you can make a list as follows: 


sketch number        number of squares           formula

1                   3                            2 * 1 + 1
2                   5                            2 * 2 + 1
3                   7                            2 * 3 + 1
4                   9                            2 * 4 + 1
5                   11                           2 * 5 + 1
6                   13                           2 * 6 + 1
.
.
.
n                   2 * n + 1


your next number of squares will always be 1 more than 2 times the sketch number.