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Worked solution

Find a distant arithmetic term

Find the twentieth term of the arithmetic progression 7,13,19,25,…7,13,19,25,\ldots.

CJC · Sequences and Series · Example 6

Answer

u20=121u_{20}=121.

Compare your reasoning

Identify first term and common difference

a=7,d=13−7=6a=7,\qquad d=13-7=6

These are the printed source values.

Make nineteen additions of the difference

u20=7+(20−1)(6)=121\begin{aligned}&u_{20}\\ & =7+(20-1)(6)\\ & =121\end{aligned}

The initial 7 is already term one.

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