1. ## Sequences

Write an explicit expression for the n-th term of the sequence.

2,5,10,17,26,37,50,65,82,101

I know that it increases by two more than the last increase each time, ie a1-a0 = 3 and a2-a1=5 and a3-a2=7

2. Go to ths site and type in your sequence.
See what you get as an answer.
The On-Line Encyclopedia of Integer Sequences

3. Originally Posted by CalcGeek31
Write an explicit expression for the n-th term of the sequence.

2,5,10,17,26,37,50,65,82,101

I know that it increases by two more than the last increase each time, ie a1-a0 = 3 and a2-a1=5 and a3-a2=7

If the difference betwee two consecuative numbers is constant then the solution would look like $\displaystyle a_n = c_1 n + c_0$ for some constants c_0 and c_1 but because the difference of difference is 2, the the formula would look like $\displaystyle a_n = c_2 n^2 + c_1 n + c_0$

Let's look for patterns

$\displaystyle a1 = 2$
$\displaystyle a2 = 5 = 4 + 1$
$\displaystyle a3 = 10 = 9 + 1$
$\displaystyle a4 = 17 = 16 + 1$
$\displaystyle a5 = 26 = 25 + 1$
$\displaystyle a6 = 37 = 36 + 1$

see the pattern?

### 17,25,37,50,65,82,101,?

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