write an expression for the nth term of the sequence....

$\begingroup$

write an expression for the nth term of the sequence 0, 7, 16, 27, 40 It is neither geometric or arithmetic

My teacher gave us a key and I can't read his writing...please any help would be great!!

$\endgroup$ 2

4 Answers

$\begingroup$

HINT: Check the differences between consecutive terms, they are in AP.

Next time show your attempts, else you might not get any help here.

$\endgroup$ 2 $\begingroup$

Just a few thoughts that might (might not) be helpful:

$$\begin{align} 0&\\ 7 &= 0 + 7 + 0\cdot 2\\ 16 &= 7 + 7 + 1\cdot 2\\ 27 &= 16 + 7 + 2\cdot 2\\ 40 &= 27 + 7 + 3\cdot 2 \end{align} $$

$\endgroup$ 2 $\begingroup$

This is a sequence defined by (n+6)n:

(0+6)0, (1+6)1, (2+6)2, (3+6)3, ..., (n+6)n

$\endgroup$ $\begingroup$

Here is a very simple way to solve such a problem: You notice that not the terms, but the increments are in arithmetic progression. I hope you also know that when the increment is linearly increasing, then by integration, the expression will be a quadratic equation. What you can do now is: Assume a quadratic equation of the form "ax^2 + bx + c = k". Here, 'x' is the variable corresponding to the nth term of the sequence, and 'k' is the value of the nth term; now simply put n=1, 2 and 3 to obtain 3 linear equations in 'a', 'b' and 'c', which can be solved for their values. And there you have your general quadratic expression. (Pardon the crude script, it's been a while since I used LATEX. Any editing would be appreciated.)

$\endgroup$

Your Answer

Sign up or log in

Sign up using Google Sign up using Facebook Sign up using Email and Password Submit

Post as a guest

Post Your Answer Discard

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy