Maths
posted by Lucas
An arithmetic and a geometric sequence have the same first terms.(2)....and the same second term say X..The sum of the first 3 terms of the arithmetic sequence equals to the third term of the geometric sequence.Calculate the first 3 terms of each sequences

Steve
a+d = ar
3/2 (2a+2d) = ar^2
3a+3d = ar^2
3(a+d) = ar^2
3ar = ar^2
3r = r^2
r = 3
So,
a+d = 3a
d = 2a
The sequences are thus
a,3a,5a,7a,9a,...
a,3a,9a,27a,...
Note that a+3a+5a = 9a, as required
Pick a value for a, and plug and chug.
Respond to this Question
Similar Questions

math
suppose an arithmetic sequence and a geometric sequence with common ration r have the same first two terms. show that the third term of the geometric series is r^2/(2r1) tomes the third term of the arithmetic sequence 
Maths
The first term of an arithmetic sequence is 2. The first, third and eleventh terms are the first three terms of a geometric sequence. Determine the seventh term of the geometric 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 … 
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 … 
math
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 … 
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.