Find the missing f(x):

x       1  2  3   4    5

f(x)   2  5  9         32

is it 14

I think the ans is 16.Is it correct?

I also think f(x)=3^x-1/4+5x/2-3/4

hello sboosy why shud we consider only f(x) = ax³ + bx² + cx + d .......

if i consider f(x) = ax² + bx + c

i am able to get the answer but if i consider f(x) = ax + b

i am not able to

please explain why is it so

hello nuknown

sboosy is right in his approach

see u need to satisfy all the given conditions and since 4 conditions are given u hav to generate a 4 unknown equation, hence the cubic eqn.

anything less or more will lead to error

i approached the same way but probably had eror in between

What about my answer?The fun. I got also satisfied all the values in the question.Plz tell me whether it is right.

show ur method allamraju

I used the method given in 318 page of HALL & KNIGHT HIGHER ALGEBRA to find nth term of a series.If we assume values of f(x) as a series then the rth term will be f(r) and it represents the value of the fun.

Let f(4)=k then 2,5,9,k,32

                         3,4,(k-9),(32-k)       

                          1,(k-13),(41-2k).For this to be a G.P,(k-13)²=41-2kk=16

To find the nth term which is the value of the fun;

The nth term will be of the form T_n=a.3^n-1+bn+c

Using T₁=2,T₂=5,T₃=9,we get a=1/4,b=5/2,c=-3/4.

Hence f(x)=xth term=3^x-1/4+5x/2-3/4.Plz tell me whether I am right.