please explain steps to get correct answer in pic below

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03-11-2022
Mathematics

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please explain steps to get correct answer in pic below

Sagot :

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MadalynneC24161 MadalynneC24161 · Answer 1 · 2022-11-03T08:53:23-04:00

Let's use the properties of the sum:

[tex]\begin{gathered} \sum ^{11}_{i\mathop=1}(3i^2+17)=\sum ^{11}_{i\mathop{=}1}3i^2+\sum ^{11}_{i\mathop{=}1}17 \\ =3\sum ^{11}_{i\mathop{=}1}i^2+17\cdot11 \end{gathered}[/tex]

Therefore the answer is the last option.

To simplify this we use the properties listed below:

[tex]\sum ^n_{i\mathop{=}1}na_i=n\sum ^n_{i\mathop{=}1}a_i[/tex][tex]\sum ^n_{i\mathop{=}1}(a_i+b_i)=\sum ^n_{i\mathop{=}1}a_i+\sum ^n_{i\mathop{=}1}b_i[/tex][tex]\sum ^n_{i\mathop{=}1}c=cn[/tex]

Sagot :

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