Terms of sequence

Number Theory Level pending

How many terms are missing in 1 , 2 , 5 , 12 , 29 , . . . , 408 1, 2, 5, 12, 29 , . . . , 408 ?

2 1 0 5

Zeeshan Ali by Zeeshan Ali , 25, Pakistan

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2 solutions

Jonathan Narvato
Feb 12, 2015

the difference of each term is the sum of the term and its preceding term

thus, 70 and 169 are the missing terms. Ans:2

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Zeeshan Ali
Jan 26, 2015

f(1)=1,f(2)=2 f(3)=f(1)+2f(2)=1+2 2=5 f(4)=f(2)+2f(3)=2+2 5=12 f(5)=f(3)+2f(4)=5+2 12=29 f(6)=f(4)+2f(5)=12+2 29=70 ----->(missing 1) f(7)=f(5)+2f(6)=29+2 70=169 ----->(missing 2) f(8)=f(6)+2f(7)=70+2 169=408

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