progression challenge.
Algebra
Level
1
The numbers 1,b,c form an arithmetic progression and the numbers 1,b,c+1 form a geometric progression. Find c.
The answer is 3.
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1 solution
We know that 2b=1+c and b2=1.(c+1)=1+c=2b. Therefore either b=0 or b=2. But 0 cannot be a member of a geometric progression, so the only option left is b=2. Then the arithmetic progression is 1,2,c or 1+c=2.2 => c=3.