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+(kn-1)d = 11

1 + (k-1)(1/3) = 11

3 + k-1 = 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. 528+245=_____ I got 107+6...
- 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 ...
- Sequences - An arithmetic sequence has first term of 6 and difference of 8; what...
- 8th Grade Algebra-Radicals:Answer Check - 4. 311 + 411 Answer: 811 7. 72...
- precal - what is the 7th geometric sequence when a10 is 9 and a13 is -72
- math - term given by x+2,3x-1,and 4x-1 form an arithmetic sequence. find the ...
- Chemistry - Calculate the amount (g) of each of the following salts that need to...
- Algebra 2 math - What is the 32nd term of the arithmetic sequence where a1 = 12 ...