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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.
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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".