If all the dolls fit in the windowsill the sum of their diameters must be less than or equal to 92 cm — the length of the windowsill.
Sum of diameters≤ 92 cm
We have a formula that describes the doll's diameter given their position in the matryoshka doll. The constant of this formula tells us the innermost doll's diameter.
t(n)= 13+3(n-1)
Since the formula is describing an arithmetic sequence, we can use the formula for calculating the sum of an arithmetic sequence to determine the sum of their diameters.
S_n=n(a_1+a_n)/2
We already know the diameter of the innermost doll. To find the diameter of the outermost doll, we will substitute n=20 into the formula.
The total diameter of the dolls is 830 millimeters, which is the same thing as 83 cm. Since this is less than 92 cm, the dolls will fit on the windowsill.
