I am a sequence of numbers where each term after the first is found by adding the two previous terms. If my fourth term is 10, what is my first term?
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Let terms be a, b, a+b, 2a+3b, etc. The fourth term is 2a + 3b = 10. Testing small positive integers, if b=2 and a=2, 2(2)+3(2)=10. Sequence: 2, 2, 4, 6... wait, Fibonacci-like: if a=1, b=3, term 3=4, term 4=7. Let's check a=1, b=3: terms are 1, 3, 4, 7 (not 10). Let's check a=2, b=2: 2, 2, 4, 6. Let's check a=1, b=something: terms are x, y, x+y, x+2y, 2x+3y = 10. If x=2, y=2: 2,2,4,6. If x=1, 2(1)+3y=10 -> 3y=8 (no). If x=2, 2(2)+3y=10 -> 3y=6 -> y=2. Sequence: 2, 2, 4, 6. Wait, standard Fibonacci definition: term 1=a, term 2=b, term 3=a+b, term 4=a+2b. So a+2b = 10. If b=3, a=4 (4,3,7,10... first term is 4). If b=2, a=6. If b=1, a=8. Let's re-verify: sequence: 4, 3, 7, 10. 4+3=7, 3+7=10. First term is 4.
About this riddle
Math riddles hide a calculation inside a short story. Pull out the numbers, work out what is being asked, and watch for a trick such as a unit change.
Difficulty: Hard. More like this: Math riddles with answers or try Target 24 for a different kind of puzzle.
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