Can layers

Cans are stored in n-layers above each other according to the arithmetic sequence. There are 37 cans in the tenth layer and a total of 190 cans in all ten layers. How many cans are in the first layer?

b) total in all n layers
c) express the given sequence in terms of recurrence relations

Final Answer:

a₁ =  1

Step-by-step explanation:

$$\begin{gathered} a_{10}=37 \\ s=190 \\ d=1 \\ s=(a_{10}+a_1)/2\cdot 10 \\ {a}_1=s/10\cdot 2-a_{10}=190/10\cdot 2-37=1 \\ a(n)=a(n-1)+d \end{gathered}$$

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