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I was looking at my notes and I think I did this wrong before. Shouldn't it be 48?

$2(a_0 + \sum_{i=1}^{4} a_k) + 30 = 48$

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    Yes, it should read $\sum_0^4(2a_k + 3 b_k) = 2(a_0 + \sum_1^4 a_k) + 3\sum_0^4 b_k = 2(2 + 7) + 3(10) = 48$ – 2017-02-13
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    Note that the other answer is consistent with $a_0 = -2$ (rather than $2$), so the the disagreement could have arisen from a sign mistake. – 2017-02-14

2 Answers 2

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Yes, indeed the answer should be $48$. Since $\sum_{k=1}^4 {a_k}=7$ and $a_0=2$: $$\sum_{k=0}^4 a_k=a_0+\sum_{k=1}^4 a_k=7+2=9$$

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You are right. It should be $$\sum_{k=0}^4 2 a_k +3 b_k = 2 \cdot (7\color{#f00}{+}2) + 3 \cdot 10 =48.$$