Answer: B, C, E
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The difference between consecutive terms (numbers that come after each other) in arithmetic sequences is the same. That means you add the same number every time to get the next number. To figure out which choices are arithmetic sequences, just see if the differences are the same.
Choice A) 1, -2, 3, -4, 5, ...
-2 - 1 = -3
3 - (-2) = 5
The difference is not constant, so it is not an arithmetic sequence.
Choice B) 12,345, 12,346, 12,347, 12,348, 12,349, ...
12,346 - 12,345 = 1
12,347 - 12,346 = 1
The difference is constant, so it is an arithmetic sequence.
Choice C) <span>154, 171, 188, 205, 222, ...
171 - 154 = 17
188 - 171 = 17
The difference is constant, so it is an arithmetic sequence.
Choice D) </span><span>1, 8, 16, 24, 32, ...
8 - 1 = 7
16 - 8 = 8
</span>The difference is not constant, so it is not an arithmetic sequence.
Choice E) <span>-3, -10, -17, -24, -31, ...
-10 - (-3) = -7
-17 - (-10) = -7
</span>The difference is constant, so it is an arithmetic sequence.
14^(7x) = 17^(-8-x)
Take the log of both sides:
7x*log 14 = -(8+x)*log 17, or 7x^log 14 = -8*log 17 - x*log 17.
Grouping the x terms, we get x(7*log 14 + log 17)= -8*log 17
Then:
-8*log 17
x= -------------------------- (answer)
7*log 14 + log 17
The expressions formed are,
- 12f -5
- (k+6)/2
- x²-x+5
- ab+3c
- 24xy+g
Formation of expressions in 1, 2 and 3:
In 1, twelve times f is, 12f
Taking away 5, it becomes (12f-5)
In 2, sum of k and 6 is, (k+6)
One-half of the above quantity is, (k+6)/2
In 3, sum of 5 with x is, (x+5)
Now, x squared minus the above expression indicates (x²-x+5)
Formation of expressions in 4 and 5:
In 4, product of a and b, is ab and 3 times c is 3c
Sum of the expressions evaluated in the previous statement = ab+3c
In 5, 24 times the product of x and y is, 24xy
Adding, g in the above computed expression, we get, 24xy+g
Learn more about expressions here:
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