mathematics, science & mathematics

RiRi Asked:

Determine the number of dots in the 30th step ...

Determine the number of dots in the 30th step following the pattern,but do not draw all 30 steps.

Explain how you could find the number of dots in step 30 without drawing them, what would the number of dots be in the 30th step. Write an algebraic expression for the number of dots in the 30th step.

step 1: **** (4)

step 2: *** *** *** (9)

step 3: **** **** **** **** (16)

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Answers

Ian Answered:

Try to relate the number of dots to the step number.
The numbers of dots are square numbers.
It would have been easier if step 2 had been 4 dots
But we can see that 2, 3 and 4 are

1 more than the step number.

Combining these ideas:-
step 1: 4 = (1 + 1)^2
step 2: 9 = (2 + 1)^2
step 3: 16 = (3 + 1)^2

If the pattern does not change
step n: number of dots = (n + 1)^2
If n is 30, number of dots = 31^2 = 961

Regards - Ian