math
posted by Brainblocked .
in an arithmetic sequence the common difference is equal to 2.the first term is also the first term of a geometric sequence. the sum of the first 3 terms of an arithmetic sequence and the sum of the first 9 terms of an arithmetic sequence form the 2nd and 3rd terms of a geometric sequence respectively determine the first 3 terms of the geometric sequence...How do I go about solving this?

math 
Reiny
first term: a
common difference = 2
sum of first 3 terms
= a + a+d + a+2d
= 3a + 6
sum of first 9 terms
= (9/2)(2a + 8(2))
= 9(a + 8)
= 9a + 72
so 3a+6 = ar
and 9a+72 = ar^2
square 3a+6 = ar^2
9a^2 + 36a + 36 = a^2r^2
r^2= (9a^2 + 36a + 36)/a^2
from the other equation,
r^2 = (9a+72)/a
(9a^2 + 36a + 36)/a^2 = (9a+72)/a
both sides times a
(9a^2 + 36a + 36)/a = (9a+72)
crossmultiply
9a^2 + 36a + 36 = 9a^2 + 72a
36a = 36
a = 1
in 3a+6 = ar
3+6 = r
r = 9
So the first 3 terms of the GS are 1 , 9, and 81
check:
sum of first 3 terms of AS=1 + 3 + 5
sum of first 9 terms of AS = (9/2)(2 + 16) = 81
Well, that checked out nicely.
Respond to this Question
Similar Questions

Precalculus
The 8th term in an arithmetic sequence is 5, and the sum of the first 10 terms is 20. Find the common difference and the first term of the sequence. Alright so in an arithmetic squence the difference d between any two successive numbers … 
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 … 
Can someone help me?!
The 1st, 5th and 13th terms of an arithmetic sequence are the first three terms of a geometric sequence with a common ratio 2. If the 21st term of the arithmetic sequence is 72, calculate the sum of the first 10 terms of the geometric … 
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 … 
Algebra
Determine whether each sequence is arithmetic or geometric. Find the next three terms. 14, 19, 24, 29, . . . A.geometric, 34, 39, 44 B.arithmetic, 32, 36, 41 C.arithmetic, 34, 39, 44 D.The sequence is neither geometric nor arithmetic. … 
math
Determine whether each sequence is arithmetic or geometric. Find the next three terms. 1. 14, 19, 24, 29, . . . (1 point) geometric, 34, 39, 44 arithmetic, 32, 36, 41 arithmetic, 34, 39, 44 *** The sequence is neither geometric nor … 
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 Help!!!
determine whether each sequence is arithmetic or geometric. find the next three terms. 1. 14,19,24,29.... geometric, 34,39,44 arithmetic,32,36,41 arithmetic 34,39,44**** the sequence is nether geometric nor arithmetic 2. 4,8,16,32.... … 
math
The 1st,5th,13th term of an arithmetic sequence are the first 3 terms of geometric sequence with a common ratio of 2. If the 21st term of the arithmetic sequence is 72, calculate the sum of the first 10 terms of the geometric sequence. 
Algebra
I am so lost on these problems. Write a geometric sequence that starts with 3 and has a common ratio of 5. What is the 23rd term in the sequence. Write an arithmetic sequence that has a common difference of 4 and the eighth term is …