7. Given the recursive sequence an = an-1 – 19 for all n > 1, where ao -14, i. Find a1, a2, a3 using the recurrence relation. ii. Use either a shortcut (that we talked about in the notes) or iteration to obtain an explicit formula for an. If you use a shortcut, specify whether the recurrence sequence is arithmetic or geometric. If you use iteration, explain your reasoning. iii. Use the explicit formula from part (ii) to find a500-

7. Given the recursive sequence an = an-1 – 19 for all n > 1, where ao -14, i. Find a1, a2, a3 using the recurrence relation. ii. Use either a shortcut (that we talked about in the notes) or iteration to obtain an explicit formula for an. If you use a shortcut, specify whether the recurrence sequence is arithmetic or geometric. If you use iteration, explain your reasoning. iii. Use the explicit formula from part (ii) to find a500-

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Description: 7.Given the recursive sequence an = an-1 – 19 for all n > 1, where ao =-14,i. Find a1, a2, a3 using the recurrence relation.ii. Use either a shortcut (that we talked about in the notes) or iteration to obtain an explicitformula for an. If you use a

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Sequence and Series

A sequence is defined as a collection of things. Series is defined to sum the things one by one in the sequence. It was invented by German mathematician Carl Friedrich Gauss.

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7.
Given the recursive sequence an = an-1 – 19 for all n > 1, where ao =-14,
i. Find a1, a2, a3 using the recurrence relation.
ii. Use either a shortcut (that we talked about in the notes) or iteration to obtain an explicit
formula for an. If you use a shortcut, specify whether the recurrence sequence is arithmetic or
geometric. If you use iteration, explain your reasoning.
iii. Use the explicit formula from part (ii) to find a500-

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Q6. Please explain clearly step by step
Scientists have developed a recursion formula to determine the number of insects in a given population for each interval, n, of time, . an = kan-1(1-an-1), where k is a constant called the Malthusian factor. a. Assuming n is measured in weeks, calculate the insect population for weeks 2, 3, and 4 if the initial population is 112, and the Malthusian factor for this population is -9.5.
ᴅᴜʀɪɴɢ ꜱᴀʟᴇꜱ ʜᴏᴜʀ ɪɴ ᴀ ꜱᴜᴘᴇʀᴍᴀʀᴋᴇᴛ, ᴄʏɴᴛʜɪᴀ ᴍᴇᴀꜱᴜʀᴇꜱ ʜᴇʀ ᴜʀɢᴇɴᴄʏ ꜰʀᴏᴍ ʙᴜʏɪɴɢ ᴢ ʙᴀɢꜱ ᴏꜰ ᴄᴀɴᴅɪᴇꜱ ᴀɴᴅ ʏ ʙᴀʀꜱ ᴏꜰ ᴄʜᴏᴄᴏʟᴀᴛᴇ ᴜꜱɪɴɢ ᴛʜᴇ ꜰᴏʟʟᴏᴡɪɴɢ ꜰᴜɴᴄᴛɪᴏɴ: ꜰ(x, ʏ) = √xʏ. ɪꜰ ᴄʏɴᴛʜɪᴀ ʜᴀꜱ ᴜꜱᴅ 5.00 ᴛᴏ ꜱᴘᴇɴᴅ ᴀɴᴅ ᴇᴀᴄʜ ʙᴀɢ ᴏꜰ ᴄᴀɴᴅɪᴇꜱ ᴀɴᴅ ᴇᴀᴄʜ ʙᴀʀ ᴏꜰ ᴄʜᴏᴄᴏʟᴀᴛᴇ ᴄᴏꜱᴛ ᴜꜱᴅ 1.50 ᴀɴᴅ ᴜꜱᴅ 1.00, ʀᴇꜱᴘ., ʜᴏᴡ ᴍᴀɴʏ ʙᴀɢꜱ ᴏꜰ ᴄᴀɴᴅɪᴇꜱ ᴀɴᴅ ʙᴀʀꜱ ᴏꜰ ᴄʜᴏᴄᴏʟᴀᴛᴇ ꜱʜᴏᴜʟᴅ ꜱʜᴇ ᴘᴜʀᴄʜᴀꜱᴇ ᴛᴏ ᴍᴀxɪᴍɪᴢᴇ ʜᴇʀ ᴜʀɢᴇɴᴄʏ? ᴜꜱᴇ ʟᴀɢʀᴀɴɢᴇ ᴏᴘᴛɪᴍɪᴢᴀᴛɪᴏɴ ᴛᴏ ꜱᴏʟᴠᴇ ᴛʜɪꜱ ᴘʀᴏʙʟᴇᴍ. (ɴᴏᴛᴇ: ꜰʀᴀᴄᴛɪᴏɴᴀʟ ɴᴜᴍʙᴇʀ ᴏꜰ ʙᴀɢꜱ ᴀɴᴅ ʙᴀʀꜱ ᴄᴀɴ ʙᴇ ᴘᴜʀᴄʜᴀꜱᴇᴅ.)
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Q1 A
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