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Question Number 128907 by bramlexs22 last updated on 11/Jan/21

$$\mathrm{Given}{\mathrm{U}}_{\mathrm{n}}=\{\begin{array}{l}2\mathrm{n}+1;\mathrm{n}\mathrm{even}\\ 3\mathrm{n}+3;\mathrm{n}\mathrm{odd}\end{array}$$$$\mathrm{The}\mathrm{value}\mathrm{of}{\mathrm{U}}_3+{\mathrm{U}}_6+{\mathrm{U}}_7+{\mathrm{U}}_{10}+{\mathrm{U}}_{11}+$$$${\mathrm{U}}_{14}+...+{\mathrm{U}}_{27}+{\mathrm{U}}_{28}=?$$

Answered by Olaf last updated on 11/Jan/21

$$$$$$\mathrm{S}=\underset{k=3}{\sum ^{k=28}}{\mathrm{U}}_k$$$$\mathrm{S}=\underset{n=1}{\sum ^{n=13}}[{\mathrm{U}}_{2n+1}+{\mathrm{U}}_{2n+2}]$$$$\mathrm{S}=\underset{n=1}{\sum ^{n=13}}[(3(2n+1)+3)+(2(2n+2)+1)]$$$$\mathrm{S}=\underset{n=1}{\sum ^{n=13}}(10n+11)$$$$\mathrm{S}=10\frac{13\times 14}{2}+11\times 13=910+143=1053$$

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