## anonymous 4 years ago i need help with a math pattern

1. amistre64

fibonnacci?

2. anonymous

no, it's an algebra pattern question about terms of a pattern

3. amistre64

it might be useful if you give us the question so that we have a better understanding of it

4. anonymous

Here's the question: The first 50 terms of a pattern sum to 2000. a) Describe the pattern. b) Describe how you found the sum. c) Give the 100th term of the pattern. d) List all the patterns that you found.

5. amistre64

well, there are 2 sequence summations that we can use; and arithmatic and a geometric

6. anonymous

we haven't been doing geometry, so it's probably the arithmatic

7. amistre64

$\sum_{n=1}^{50}a_1+d(n-1)=\frac{50(a_1+a_{50})}{2}$

8. amistre64

$\sum_{n=1}^{50}a^1*r^{n-1}=a_1\frac{1-r^50}{1-r}$

9. anonymous

this is a 6th grade homework question

10. amistre64

r^(50) that is; forgot to wrap it in a {}

11. anonymous

i'm not following you

12. amistre64

lets do arith then :) $\frac{50(a_1+a_{50})}{2}=2000$ ${25(a_1+a_{50})}{}=2000$ ${a_1+a_{50}}{}=2000/25$ ${a_1+a_{50}}{}=80$ sound good?

13. anonymous

ok, thanks for your help. so then we could set any number as the first term and go from there?

14. amistre64

correct; choose any 2 numbers that add up to 80; and work in the summation rule for the rest of it to get the details of the common difference

15. anonymous

ok, that works. thanks again

16. amistre64

$a_{80}=a_1+d(80-1)$