# Sequences – 9 ## 7 thoughts on “Sequences – 9”

1. Rohit |

Sir, can this question be solved with Calculus?

2. rohipedia |

Sir, can this question be solved using Calculus?

• catcracker |

Perhaps, but it seems too much effort (quite aside from being out of scope for CAT)? It is a discrete problem, not a continuous one..

regards
J

3. Ajay Athreya |

How did you arrive at that expression an^2+bn+c for the nth term?

• catcracker |

I mentioned the calculus-based justification for that. A rigorous non-calculus based proof would be more painful; please take my word for it that it will be of this form if you don’t like calculus 🙂

regards
J

4. seema |

sir, as you mentioned it can be solved thru calculus, so I tried solving it in two ways, one gave the correct answer, other didn’t, can you please explain why this happened?
1) WRONG
T2 = 4 = 2 ax + b (first derivative) (keeping n=2),
we get 4=4+b;
so, b=0
2) RIGHT
taking second order derivative of ax^2+bx+c = 0,
2a = 2 (second order difference is 2)
a = 1,
now solving the two equations keeping value of a in it.
t1 = a + b + c = 3 and t2= 4a + 2b + c = 5,
at a =1, becomes
b + c = 2
2b + c = 1
we get, b= -1 and c = 3

• catcracker |

T2 is not the first derivative :P. T2 is the second term. Also your “a” seems to have vanished in this step
“4 = 2 ax + b (first derivative) (keeping n=2),
we get 4=4+b;”
but that is irrelevant as anyway you are applying it wrong to begin with. You don’t apply derivative at any random point of your choice.