math
posted by Brittany .
The third and seventh terms of an arithmetic sequence are 10 and 20.
1) What is the value of the 1st term?
2) What is the value of the 9th term?
3) What is the equation to find the nth term in the sequence?
HELP!! PLEASE!!

Arithmetic sequence
a, a + d, a + 2d, a + 3d, ...a +(n  1)d
1)a3 = 10, a7 = 20
Since these are 4 places apart (7  3 = 4)
a7 = a3 + 4d
20 = 10 + 4d
10 = 4d
d = 10/4 = 2.5
So, the common difference, d = 2.5
To find the 1st term a,
a3 = a + 2d
10 = a + 2(2.5)
10 = a + 5
a = 5
2) to find 9th term
a9 = a + 8d
a9 = 5 + 8(2.5)
a9 = 5 + 20
a9 = 25
3) nth term
Last term = a + (n  1)d
an = 5 + (n  1)(2.5) 
4a2
Respond to this Question
Similar Questions

Mathematics : Arithmetic Sequence
The 5th term and the 8th term of an arithmetic sequence are 18 and 27 respctively. a)Find the 1st term and the common difference of the arithmetic sequence. b)Find the general term of the arithmetic sequence. 
Math
A sequence is formed by adding together the corresponding terms of a geometric sequence and and an arithmetic sequence.The common ratio of the geometric sequence is 2 and the common difference of the arithmetic sequence is 2.The first … 
Arithmetic Sequence
Given the third term of an arithmetic sequence less than the fourth term by three. The seventh term is two times the fifth term. Find the common difference and the first term. 
Maths
1..The first 2 terms of a geometric progression are the same as the first two terms of an arithmetic progression.The first term is 12 and is greater than the second term.The sum of the first 3 terms od the arithmetic progression is … 
Precalculus
1. In an arithmetic sequence, the fifth term, u5, is greater than the first term, u1. The difference between these terms is 36. a) find the common difference 9? 
Math
1. Find the 12th term of the arithmetic sequence 2, 6, 10, … . 2. Solve for the 101st term of the sequence whose 1st term is xy and d=2x+y3. 3. In the sequence 2, 6, 10, … , what term has a value of 106? 
maths
The fifth term of an arithmetic sequence is 23 and the 12th term is 72. And they say first question 1.determine the first three terms of the sequences and the nth term. 2.what is the value of the 10th term. 3. Which term has a value … 
maths
The fifth term of an arithmetic sequence is 23 and 12th term is 72. And they say 1. Determine the first three terms of the sequences and the nth term. 2. What is the value of the 10th term. 3. Which term has a value of 268. 
math
in an arithmetic sequence 17th term is 9 times the first three terms and the 9th term is 6 less than 3 times the 1st term. Find the first three terms 
Math
The third term of an arithmetic sequence is 12 and the seventh term is 8.what is the sum of the first 10 terms?