SOLUTION: I'm a high school student in Algebra 2. I have a couple questions, 1. what are the formulas to find the nth term of an arithmetic and geometric sequence? here is a problem im hav

Question 489968: I'm a high school student in Algebra 2. I have a couple questions,
1. what are the formulas to find the nth term of an arithmetic and geometric sequence? here is a problem im having trouble with..
write a formula for the nth term of an arithmetic sequence, then a25.
d=2 a12=18
an=_____
a25=_____
I'm not really confident on how to find the answer :(
Another question I have is how to find the sum..
ex. find the sum of the first n terms when n=20.
arithmetic series: 40+37++34+31+....
then im supposed to find n for Sn=195, how do i do that??
thanks for the help!
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
1. what are the formulas to find the nth term of an arithmetic and geometric sequence? here is a problem im having trouble with..
write a formula for the nth term of an arithmetic sequence
a(n) , then a25.
when d=2 and a(12) = 18
Ans: an=a(1)+(n-1)d
----
Since a(12) = a(1)+11*2 = 18
a(1) = 18 - 22 = -4
--------------------------
Ans: a25= a(1)+24d
a(25) = -4+24*2
a(25) = 44
===================
Another question I have is how to find the sum..
ex. find the sum of the first n terms when n=20.
arithmetic series: 40+37+34+31+....
--
S(n) = (n/2)[(a(1)+a(n)]
a(1) = 40
d = -3
a(n) = a(20) = 40+(19)*-3 = -17
----
S(20) = (20/2)[40-17] = 10[23] = 230
========================================

then im supposed to find n for S(n)=195, how do i do that??
a(n) = 40 + (n-1)(-3) = 40-3n+3 = 43-3n
Solve: (n/2)(40 + 43-3n) = 195
(n/2)(83-3n) = 195
n(83-3n) = 390
-3n^2 + 82n - 390 = 0
---
Solve for "n":
Use the quadratic formula to get the whole number answer.
Ans: n = 6
==================
Cheers,
Stan H.
===============

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