The lengths

The lengths of the twelve poles form an Arithmetic Progression (A. P). If the third pole is 3m and the eighth pole is 5 m, find the
(i) Length of the first pole
(ii) Sum of the length of the poles

Final Answer:

a₁ =  2.2 m
s =  52.8 m

Step-by-step explanation:

$$\begin{gathered} AP \\ n=12 \\ {a}_3=3\text{m} \\ {a}_8=5\text{m} \\ {a}_3=a_1+2\cdot d \\ {a}_8=a_1+7\cdot d \\ 3=a_1+2\cdot d \\ 5=a_1+7\cdot d \\ {a}_1+2d=3 \\ {a}_1+7d=5 \\ Row2-Row1\to Row2 \\ 5d=2 \\ d=\frac{2}{5}=0.4 \\ {a}_1=3-2d=3-2\cdot 0.4=2.2=\frac{11}{5}\text{m}=2.2\text{m} \\ {a}_1=\frac{11}{5}=2.2 \\ d=\frac{2}{5}=0.4 \end{gathered}$$

$$\begin{gathered} a_{12}=a_1+11\cdot d=2.2+11\cdot 0.4=\frac{33}{5}=6.6\text{m} \\ s=\frac{a_1+a_{12}}{2}\cdot n=\frac{2.2+6.6}{2}\cdot 12=\frac{264}{5}\text{m}=52.8\text{m} \end{gathered}$$

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