SOLUTION: What is the nth term for the following sequence: 10, 30, 60, 100, 150, 210, ...

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Question 1182229: What is the nth term for the following sequence:
10, 30, 60, 100, 150, 210, ...
Found 3 solutions by greenestamps, MathLover1, Edwin McCravy:
Answer by greenestamps(13198)   (Show Source):
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If each term is divided by 10, the sequence is

1, 3, 6, 10, 15, 21, ...

You might recognize that sequence as the triangular numbers; or as the sequence in which the n-th term is the sum of the integers 1 through n.

The formula for the n-th triangular number is

So the n-th term of this sequence is

ANSWER:

Answer by MathLover1(20849)   (Show Source):
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given: ,,,,,
Sequence : ...................................
First diff. : .........................................
Second diff. : ..................................

We see that the second differences are all equal so we concludet that this is a quadratic sequence.
The quadratic sequence has the form:

To find the value of we just divide second difference ( ) with .

Now we have:

Substitute and into above equation:
if ,

....eq.1

if ,

.....eq.2
from eq.1 and eq.2 we have

go to
....eq.1, substitute

then nth term equation is:

Answer by Edwin McCravy(20054)   (Show Source):
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10, 30, 60, 100, 150, 210, ... Find the sequence of differences to see if it is an arithmetic sequence 30-10, 60-30, 100-60, 150-100, 210-150, ... Simplifying 20, 30, 40, 50, 60, ... This is an arithmetic sequence, so the nth term is quadratic: Substitute n=1,2,3, a_n = 10, 20 and 30 That gives us the system of equations to solve: The solution is A=5, B=5, C=0 So the nth term becomes or Edwin