topsquark

C'mon people! It's a trick question. It is intuitively obvious that f(3)= 87653 (note the pattern of 87653.) Clearly we can immediately say:
$\displaystyle f(x) = \frac{87647}{120} x^4 - \frac{1139411}{60} x^3 + \frac{21999517}{120} x^2 - \frac{46715911}{60} x + 1227058$

Thus f(3) = 87653.

-Dan

manishsqrt

The answer is 6, 3*2=6.

Country Boy

Do you care, Denis?

Denis

Deeply...losing sleep over this...

mehak ahuja

Ans is 6 for sure...
8*7=56
7*6=42
6*5=30
5*4=20
4*3=12
3*2=6

Denis

Geezzzzzzzz......................

acubed123

It turns out that the '?' can be whatever we want it to be!

Allow me to illustrate. Take for example, f(x)=(1/40)x^4-(13/20)x^3+(291/40)x^2-(553/20)x+42, and evaluate f(8.), f(7), f(6), f(5), f(3). It turns out that:

f(8.)=56,
f(7)=42,
f(6)=30,
f(5)=20,
f(3)=9.

Wait, what sorcery is this? Turns out that although the popular rule f(x)=x(x-1), which gives f(x)=6, satisfies the known values in the sequence, that f(x)=(1/40)x^4-(13/20)x^3+(291/40)x^2-(553/20)x+42 also satisfies them--except with a different value of f(3)!

Here's another one that also works but gives f(3)=12:
f(x)=(1/20)x^4-(13/10)x^3+(271/20)x^2-(543/10)x+84

And here is one where f(3)=π
f(x)=(1/120)(π-6)x^4-(13/60)(π-6)x^3+(1/120)(251π-1386)x^2+(1/60)(3138-533π)x+14(π-6)

Finally, in general if you want the '?'=k, i.e., f(3)=k where k is the value of your choice, then
(1/120)(k-6)x^4-(13/60)(k-6)x^3+(1/120)(251k-1386)x^2+(1/60)(3138-533k)x+14(k-6)

More details here:
https://www.scribd.com/doc/260182194...tary-Sequences

. . . I know what you're thinking, "But you just generated the pattern using a fourth degree polynomial--anybody can do that!" Hence, I present to you a non-polynomial alternative . . .

Country Boy

Yes, given a finite number of data points there exist an infinite number of functions giving those values.

rebeccaspears

This is the basic question in Maths. The simplest way of answer it is already posted.

Just look out the question,

8=56
7=42
6=30
5=20
3=?

If you see that the answer comes from the descending multiplication way.

8=56 (8*7=56)
7=42 (7*6=42)
6=30 (6*5=30)
5=20 (5*4=20)
4=12 ( 4 is missing here, just put 4)
3=? the answer 6 because 3*2=6

If you want to learn more tricky questions. Connect with a tutor who helps you to solve these questions and help in your exams and as well as in homework.

mary canty

if 8*7then 56
7*6=42
6*5=30
5*4=20
so
3*2 will be 6