Help with this Arithmetic Series Question??

goldendeer04

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I've recently had a test that was incredibly difficult. My teacher is going to give us 30 more minutes to finish it tomorrow and I really need help with this question. These are all the details I can remember, I hope it's enough!

Q: Find t1 and the common difference of an arithmetic series. The sum of S5 and S6 equals 18. t6 is greater than t3 by 9.

Anything will help... thank you in advance!!
 
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I've recently had a test that was incredibly difficult. My teacher is going to give us 30 more minutes to finish it tomorrow and I really need help with this question. These are all the details I can remember, I hope it's enough!

Q: Find t1 and the common difference of an arithmetic series. The sum of S5 and S6 equals 18. t6 is greater than t3 by 9.

Anything will help... thank you in advance!!
Please show us what you have tried and exactly where you are stuck.

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Test or not, nobody here will do this problem for you. We will help you so please show us what you know about solving this problem. Thanks for being honest by saying it is for a test.
 
What do "S5" and "S6" mean? Are they the sum of the first 5 terms and sum of the first 6 terms where "t6" and "t3" are the individual terms"? Do you know what an "arithmetic sequence" is?

Writing "a" as the first term and "d" as the common difference, write down the first six terms of the sequence. From that write a simple formula for the sum of the first five terms and another for the sum of the first six terms. Add them together and set that equal to 18. That gives you one equation for a and r.

Now, subtract the third term from the sixth term and set that equal to 9.

You now have two equations to solve for a and d.
 
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