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Hello,Can you please help me with question # 25 in the picture?Thank you

Hello,Can you please help me with question # 25 in the picture?Thank you-example-1

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To find the sum of an arithmetic sequence up to the nth term, we use the sum formula, which is


S_n=n((a_1+a_n)/(2))

where a1 represents the first term, and an the nth term.

The general term of our sequence is


a_n=3n+2

We want to sum up to the 16th term. Evaluanting n = 16 and n = 1 on this expression, we get the terms to plug in our formula


\begin{gathered} a_1=3(1)+2=3+2=5 \\ a_(16)=3(16)+2=48+2=50 \end{gathered}

Then, the sum is equal to


\sum_{i\mathop{=}1}^(16)(3i+2)=16((50+5)/(2))=8\cdot55=440

The result of this sum is 440.

User Dmitry Guselnikov
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