[administration]

Let f(x) be a sixth degree polynomial which has the coefficient of the highest power of x as 1. If f(1) = 7, f(2) = 10, f(3) = 13, f(4) = 16, f(5) = 19, f(6) = 22, then the value of f(7) is

25
745
750
none of these??

[Wonder Boy]

Here we see , we have 6 equations and 6 variables .. so it seems to be a solvable problem but it would take a lots of time. so surely it would not be a CAT problem . But wait. check the trend of the values and you will find out you can solve it in 30 seconds.

 

The problem says  f(1) = 7, f(2) = 10, f(3) = 13, f(4) = 16, f(5) = 19, f(6) = 22

all have a difference of 3. 7+3=10+3=13+3=16+3=19+3=22

 

so f(x) = 3x+4 (for x=1,2,3,4,5,6)

Since f(x) is a six degree polynomial so we can write f(x) as

f(x) = a(x-1)(x-2)(x-3)(x-4)(x-5)(x-6) + 3x+4 (for x=1 to inf)

Since coefficient of highest power of x = 1, so a = 1.

Hence f(7) = 6.5.4.3.2.1 + 25 = 745.

[Author]

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