Posted by Jared on Wednesday, September 30, 2009 at 8:56pm.
suppose that a1, a2, a3, ..., ak forms an arithmetic sequence. If a5+a8+a11=10, a7+a10+a13=12, and ak=11, find k
note: the numbers and the k after the a's are subscript but i don't know how to type that

advanced math  Reiny, Wednesday, September 30, 2009 at 9:08pm
from your first equation :
a+4d + a+7d + a+10d = 10
3a + 21d = 10 (#1)
from your second equation :
a+6d + a+9d + a+12d = 12
3a 27d = 12 (#2)
subtract #2  #1
6d = 2
d = 1/3
back in #1, 3a + 21(1/3) = 10
a = 1
then a+(kn1)d = 11
1 + (k1)(1/3) = 11
3 + k1 = 33
k = 31
check : term(31) = a+30d
= 1 + 30(1/3)
= 1 + 10 = 11 Yea!!!
Answer This Question
Related Questions
 Math  Can you please check these problems? 1. 5ã28+2ã45=_____ I got 10ã7+6ã...
 Precalculus  Find d of an arithmetic sequence if a(subscript 4)=14 and a (...
 Math  Problem 6: Let a1,a2,.........a10 be an arithmetic sequence. If a1+a3+a5+...
 Math  Let a1,a2,......a10 be an arithmetic sequence. If a1+a3+a5+a7+a9=17 and ...
 8th Grade AlgebraRadicals:Answer Check  4. 3ã11 + 4ã11 Answer: 8ã11 7. 7ã2...
 Sequences  An arithmetic sequence has first term of 6 and difference of 8; what...
 precal  what is the 7th geometric sequence when a10 is 9 and a13 is 72
 Chemistry  Calculate the amount (g) of each of the following salts that need to...
 math  term given by x+2,3x1,and 4x1 form an arithmetic sequence. find the ...
 Algebra 2 math  What is the 32nd term of the arithmetic sequence where a1 = 12 ...
More Related Questions