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

Question

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

Answer 1

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

Answer 2

for t(10)= a+9d .. where did you get the 9 from? & can you explain how you got 710? thank you

Answer 3

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!

Answer 4

oh sorry sorry. i never got that you simplified it. thanks

Answer 5

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

Answer 6

This was GREAT