SOLUTION: The sixth and eighth terms of an arithmetic sequence are −11 and −19. Find the fifteenth term.

Algebra.Com
Question 1178674: The sixth and eighth terms of an arithmetic sequence are
−11 and −19.
Find the fifteenth term.

Found 2 solutions by MathLover1, ikleyn:
Answer by MathLover1(20850)   (Show Source): You can put this solution on YOUR website!
th term of an arithmetic sequence is:


if the sixth and eighth terms of an arithmetic sequence are


we have


.........solve for
.......eq.1


.........solve for
.......eq.2
from eq.1 and eq.2 we have
......solve for




go to
.......eq.1, substitute




your formula is:



then the term is:









Answer by ikleyn(52788)   (Show Source): You can put this solution on YOUR website!
.

The 6th and the 8th terms represent the points -11 and -19 on the number line with the difference of 8 units between them.


There are two gaps of equal length between the 6th and the 8th terms of the AP on the number line.

Hence, the length of each gap is   = 4.



    Since the given AP is decreasing sequence, it implies that the common difference of the AP is -4.



The 15th term is in 7 gaps distance from the 8th term;  hence


     =  - 7*4 = -19 - 28 = -47.


ANSWER.   = -47.

From my post, learn how to solve such problem straightforward in short mode.


---------------

My lessons on arithmetic progressions in this site are
    - Arithmetic progressions
    - The proofs of the formulas for arithmetic progressions
    - Problems on arithmetic progressions
    - Word problems on arithmetic progressions
    - Chocolate bars and arithmetic progressions
    - Free fall and arithmetic progressions
    - Uniformly accelerated motions and arithmetic progressions
    - Increments of a quadratic function form an arithmetic progression
    - One characteristic property of arithmetic progressions
    - Solved problems on arithmetic progressions
    - Calculating partial sums of arithmetic progressions
    - Finding number of terms of an arithmetic progression
    - Inserting arithmetic means between given numbers
    - Advanced problems on arithmetic progressions
    - Problems on arithmetic progressions solved MENTALLY

Also, you have this free of charge online textbook in ALGEBRA-II in this site
    - ALGEBRA-II - YOUR ONLINE TEXTBOOK.

The referred lessons are the part of this online textbook under the topic
"Arithmetic progressions".


RELATED QUESTIONS

The second and fifth terms of an arithmetic sequence are 17 and 19, respectively. What is (answered by Theo)
the sum of the first twelve terms of an arithmetic sequence is 1188. if the sixth term is (answered by josgarithmetic)
The fourth term of an arithmetic sequence is 17, and the sixth term is 11. Find the... (answered by josgarithmetic,greenestamps)
sum of first 20 terms of an arithmetic sequence is 900. sixth term is 27. what is its... (answered by reviewermath)
The eighth term of an arithmetic sequence is 55 and the tenth term is 77. Find the third... (answered by robertb)
Two terms of an arithmetic sequence are a5=11 and a32=65. Find a rule for the nth... (answered by stanbon)
The third term of an arithmetic sequence is 8 and the sixth term is 2. Find the 30th... (answered by ikleyn,Fombitz)
Suppose that the eighth term of an arithmetic sequence is 59, and also suppose that the... (answered by mananth)
The first term of an arithmetic sequence is -3 and the fifteenth term is 53. What is the... (answered by MathLover1,MathTherapy,greenestamps,ikleyn)