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Question

Find the sum of $$15$$ terms of the series whose $$n^{th}$$ term is $$4n + 1$$.


Solution

$${ T }_{ n }=4n+1$$ 
sum $$=\sum _{ k=1 }^{ 15 }{ \left( 4k+1 \right)  } $$
$$=\sum _{ k=1 }^{ 15 }{ 4k } +\sum _{ k=1 }^{ 15 }{ \left( 1 \right)  } $$
$$=4\left[ 1+2+3+4+..........+15 \right] $$
$$=4\times \cfrac { 15\times \left( 15+1 \right)  }{ 2 } +15$$
$$=480+15$$
$$=\boxed { 495 } $$

Mathematics

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