Posted by **Mae** on Sunday, January 4, 2009 at 10:58pm.

The 10th term of an arithmetic series is 34, and the sum of the first 20 terms is 710. Determine the 25th term.

Can someone please explain how to do this? I don't know which formula to use. TIA

- Math-Gr.11 urgent -
**Reiny**, Sunday, January 4, 2009 at 11:31pm
You know t(10) = a+9d

a+9d = 34

or a = 34-9d

S(20) = 20/2[2a + 19d]

710 = 10(2a + 19d)

71 = 2a + 19d

71 = 2(34-9d) + 19d

71 = 68 - 18d + 19d

3 = d

a = 34-27 = 7

then t(25) = a+24d = 7 + 24(3) = 79

- Math-Gr.11 urgent -
**Mae**, Sunday, January 4, 2009 at 11:47pm
for t(10)= a+9d .. where did you get the 9 from? & can you explain how you got 710? thank you

- Math-Gr.11 urgent -
**Reiny**, Monday, January 5, 2009 at 12:01am
you should know that

t(n) = a + d(n-1) one of the most basic formulas in the study of sequences

and you gave me 710 in the question!

- Math-Gr.11 urgent -
**Mae**, Monday, January 5, 2009 at 12:04am
oh sorry sorry. i never got that you simplified it. thanks

- Math-Gr.11 urgent -
**Jake**, Tuesday, October 20, 2009 at 5:07pm
hi, i was wondering where you got:

20/2[2a + 19d] from, im in yr 11 but want to start revising a level because i want to get a phd in maths, so i just wanted to know where you got it from, if you could answer this, then thanks

- Math-Gr.11 urgent -
**A. S**, Sunday, November 11, 2012 at 1:36am
This was GREAT

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