Asked by Mae

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
Answered by Reiny
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
Answered by Mae
for t(10)= a+9d .. where did you get the 9 from? & can you explain how you got 710? thank you
Answered by Reiny
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!
Answered by Mae
oh sorry sorry. i never got that you simplified it. thanks
Answered by Jake
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
Answered by A. S
This was GREAT
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