posted by .

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

a+4d + a+7d + a+10d = 10
3a + 21d = 10 (#1)

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!!!

## Similar Questions

1. ### Precalculus

Find d of an arithmetic sequence if a(subscript 4)=14 and a (subscript 11)=35 I assume d is the difference between successive terms, since you have said this is an 'arithmetic' sequence. Increasing the subscript by 5 increases the …

4. 3ã11 + 4ã11 Answer: 8ã11 7. 7ã2 - 2ã8 Answer: 1ã2 ?
3. ### Algebra 2 math

What is the 32nd term of the arithmetic sequence where a1 = 12 and a13 = –60?
4. ### math

term given by x+2,3x-1,and 4x-1 form an arithmetic sequence. find the value of x. i didn't get it how to start this question and how it forms arithmetic sequence?
5. ### Chemistry

Calculate the amount (g) of each of the following salts that need to be added to a 200 mL volumetric flask to produce a 2 M solution of S. CaSO(subscript 4) [NH(subscript 4)subscript 2]SO(subscript 4) NOTE: the subscript 2 is outside …
6. ### Math

Can you please check these problems? 1. 5ã28+2ã45=_____ I got 10ã7+6ã5 2. -4ã75+3ã147=_____ I got 1ã21 3. -11ã8-7ã12=______ I got -11ã8-14ã3 4. ã150-5ã96 I got -15ã6 5. 9ã13-6ã11+ã13=___
7. ### precal

what is the 7th geometric sequence when a10 is 9 and a13 is -72
8. ### Sequences

An arithmetic sequence has first term of 6 and difference of 8; what is the tenth term?
9. ### Math

Problem 6: Let a1,a2,.........a10 be an arithmetic sequence. If a1+a3+a5+a7+a9=17 and a2+a4+a6+a8+a10=15, then find a1.
10. ### Math

Let a1,a2,......a10 be an arithmetic sequence. If a1+a3+a5+a7+a9=17 and a2+a4+a6+a8+a10=15 then find a1.

More Similar Questions