Question

Look at the steps and find the pattern.step 1step 2step 3How many dots are in the 27th step?dots

Answer 1

From the figures, notice that the number of dots increases by 7. This give us the following sequence:

$7,14,21,\ldots$

To obtain the 2nd step, we add one 7 to the first term.

$7+1(7)=7+7=14$

To obtain the 3rd step, we add two 7s to the first term.

$7+2(7)=7+14=21$

To obtain the 4th step, we add three 7s to the first term.

$7+3(7)=7+21=28$

Notice that we multiply the 7 by the difference of the nth step and 1.

Therefore, to find the 27th step, we add 26 7s to the first term.

$7+26(7)=7+182=189$

Therefore, there must be 189 dots in the 27th step.