math
posted by sdgsd .
An arithmetic series has third term 11. The ninth term is 5 times the second term. Find the common difference.

Let the first term be called a and the common difference be called b.
a + 2b = 11
a + 8b = 5*(a + b) = 5a + 5b
The last equation can be rewritten
4a  3b = 0
4a + 8b = 44
11b = 44
b = 4
a = 11  2b = 3
The series is 3,7,11,15,19,23,27,31,35...
Note that 35 (the ninth term) is 5 times 7
Respond to this Question
Similar Questions

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. 
Math
The fifth term of an arithmetic progression is three times the second term,and the third term is 10.a)What is the first term,b)the common difference and c)the 15th term? 
math
The sum of the first 10 terms of an arithmetic series is 145 and the sum of its fourth and ninth term is five times the third the..determine the first term and constant difference 
math
the fourth term of an arithmetic progression is equal to 3 times the first term and the seventh term exceeds twice the third term by 1 find the first term and the common differrence 
Algebra
True or False 1. – 5, – 5, – 5, – 5, – 5, … is an arithmetic sequence. 2. In an arithmetic sequence, it is possible that the 13th term is equal to its 53rd term. 3. In an arithmetic sequence, the common difference is computed … 
math
The sum of the first 10 term of an arithmetic sequence is 145 and the sum of the fourth and ninth term is five times the third term. Determine the first term and constant difference. 
math
if 4th term of an arithmetic progression is 3 times the 1st term nd 7th term exceeds twice the third term by 1. find the first term and common difference 
Arithmetic progession
The third term of an A.P is 10times more than the second term. Find the sum of the eight and fifteen term of the A.P if the seventh term is seven times the first term 
Math
The sum of third and ninth terms of arithmetic series is 20 and the difference between the twelfth and fourth term is 32.determine the value of the first term and the constant difference. 
arithmetic
in an arithmetic progression the 13th term is 27 and the 7th term is three times the second term find;the common difference,the first term and the sum of the first ten terms