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Sagot :
Answer:
3,-3,3,-3,3,-3
-1,½,-⅓,¼,-⅕,⅙
Step-by-step explanation:
1st Quarter namin i2 sa G10 last year, i remember this topic entitled "PATTERNS" ?
Answer and step-by-step explanation:
To find the general term of the given sequence, let's determine first if it is an arithmetic sequence or a geometric sequence.
Find the common difference to determine if it is an arithmetic sequence. Subtract each term by the previous term.
1. 3, -3, 3, _, _, -3
-3 - 3 = -6
3 -(-3) = 6
The two differences are different so there is no common difference. This is not an arithmetic sequence.
Find the common ratio to determine if it is a geometric sequence. Divide each term by the previous term.
-3 ÷ 3 = -1
3 ÷ -3 = -1
The two quotients are the same which means -1 is the common ratio of the given geometric sequence.
Let's use the geometric sequence formula to find the general term.
An = A1(r)^n-1
where
An is the nth term,
A1 is the first term,
n is the number of terms and
r is the common ratio.
Substitute the given values.
A1 = 3
r = -1
An = 3(-1)^n-1
Then use the general term to find the missing terms which is the 4th and 5th terms.
A4 = 3(-1)^4-1
A4= 3(-1)^3
A4= 3(-1)
A4= - 3
A5 = 3(-1)^5-1
A5 = 3(-1)^4
A5 = 3(1)
A5 = 3
Therefore, the general term is:
[tex]An = 3(-1) {}^{n - 1} [/tex]
The complete sequence is:
3, -3, 3, -3, 3, -3
2. -1, _, -1/3, 1/4, -1/5, _
The given sequence is neither arithemtic nor geometric. It is similar to a harmonic sequence.
Take the reciprocals of all terms and create a sequence to find the missing terms.
-1, 2, -3, 4, -5, 6
*Observe that the numbers are counting numbers which have an alternate of positive and negative sign. The negative numbers are all odd numbers and the positive numbers are all even numbers.
Flip again to make the sequence.
The general term is:
An = 1/-n where n is an odd number
and
An = 1/n where n is an even number.
The complete sequence is:
-1, 1/2, -1/3, 1/4, -1/5, 1/6
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