At week

At week 3., the turtle was 5.45 centimeters long. At week 12, the turtle was 10.20 centimeters long. From week 12 to week 21, the turtle grew 0.5 centimeters less than it grew from week 3 to week 12. What was the length in centimeters of the turtle at week 21?

Final Answer:

a₂₁ =  10.45 cm

Step-by-step explanation:

$$\begin{gathered} a_3=5.45\text{cm} \\ {a}_{12}=10.20\text{cm} \\ {a}_{12}=a_3+(12-3)\cdot d_1 \\ {d}_1=\frac{a_{12}-a_3}{12-3}=\frac{10.2-5.45}{12-3}=\frac{19}{36}\doteq 0.5278\text{cm} \\ {d}_2=d_1-0.5=0.5278-0.5=\frac{1}{36}\doteq 0.0278\text{cm} \\ {a}_{21}=a_{12}+d_2\cdot (21-12)=10.2+0.0278\cdot (21-12)=10.45\text{cm} \end{gathered}$$

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