Explanation:
A sequence is a list of numbers.
A <em>geometric</em> sequence is a list of numbers such that the ratio of each number to the one before it is the same. The common ratio can be any non-zero value.
<u>Examples</u>
- 1, 2, 4, 8, ... common ratio is 2
- 27, 9, 3, 1, ... common ratio is 1/3
- 6, -24, 96, -384, ... common ratio is -4
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<u>General Term</u>
Terms of a sequence are numbered starting with 1. We sometimes use the symbol a(n) or an to refer to the n-th term. The general term of a geometric sequence, a(n), can be described by the formula ...
a(n) = a(1)×r^(n-1) . . . . . n-th term of a geometric sequence
where a(1) is the first term, and r is the common ratio. The above example sequences have the formulas ...
- a(n) = 2^(n -1)
- a(n) = 27×(1/3)^(n -1)
- a(n) = 6×(-4)^(n -1)
You can see that these formulas are exponential in nature.
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<u>Sum of Terms</u>
Another useful formula for geometric sequences is the formula for the sum of n terms.
S(n) = a(1)×(r^n -1)/(r -1) . . . . . sum of n terms of a geometric sequence
When |r| < 1, the sum converges as n approaches infinity. The infinite sum is ...
S = a(1)/(1-r)
Answer; 47.27 Inches
Let the height of Dagne be x.
Now we are told that she can do a vertical jump that is 27.5% of her height. This is represented as 0.275x.
Now we are told the height she can jump is 13.2. Thus;
0.275x = 13.2
x = 13.2/0.275
x = 47.27 inches
ANSWER : (9u - 8)2
STEPS:
Step-1 : Multiply the coefficient of the first term by the constant 81 • 64 = 5184
Step-2 : Find two factors of 5184 whose sum equals the coefficient of the middle term, which is -144 .
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -72 and -72
81u2 - 72u - 72u - 64
Step-4 : Add up the first 2 terms, pulling out like factors :
9u • (9u-8)
Step-5 : Add up the four terms of step 4 :
(9u-8) • (9u-8)
Which is the desired factorization
Answer:
the second one, ((6 x 5) x 4) +((5 x 4) x 2) = 160
the third one, ((7 x 6) x 4) + (6 x 4) x 2) = 216
the fourth one, ((8 x 4) x 4) + ((4 x 3) x 2) = 152
Step-by-step explanation:
