The sequence where each term is found by adding or subtracting the previous term by a constant or fixed number is known as an arithmetic sequence. The constant or fixed number is called the common difference. To find the common difference in the arithmetic sequence, subtract any of the two consecutive terms. Keep in mind that you have to add if the arithmetic sequence is arranged in increasing order and subtract if it is in decreasing order.
Let us now find the next three terms in the arithmetic sequences and identify the rules in finding such terms.
A. 5, 10, 15, 20, 25, 30, 35
Rule: Add 5
Common Difference: 25 - 20 = 5
The arithmetic sequence is arranged in increasing order so to find the next terms, add 5 to the previous term.
20 + 5 = 25
25 + 5 = 30
30 + 5 = 35
B. 3, 5, 7, 9, 11, 13, 15
Rule: Add 2
Common Difference: 9 - 7 = 2
The arithmetic sequence is arranged in increasing order so to find the next terms, add 2 to the previous term.
9 + 2 = 11
11 + 2 = 13
13 + 2 = 15
C. 12, 13, 14, 15, 16, 17, 18
Rule: Add 1
Common Difference: 15 - 14 = 1
Add 1 to the previous term.
15 + 1 = 16
16 + 1 = 17
17 + 1 = 18
D. -2, -4, -6, -8, -10, -12
Rule: Add -2
Common Difference: -6 - (-4) = -6 + 4 = -2
Add -2 to the previous term.
-6 + -2 = -8
-8 + -2 = -10
-10 + -2 = -12
E. 128, 428, 928, 1628, 2528, 3628
Rule: Add 700, then add 900 and 1100 or
Add 200 to the previous difference and add the number to the previous term
This case is different from the rest. For this one, you have to find the second difference by finding the differences of the consecutive terms. Then, subtract their differences.
428 - 128 = 300
928 - 428 = 500
Second Difference: 500 - 300 = 200
Since the second difference is 200, you have to keep on adding 200 from the previous difference and add it to the previous term in the sequence.
Answers & Comments
Answer: Arithmetic Sequence
The sequence where each term is found by adding or subtracting the previous term by a constant or fixed number is known as an arithmetic sequence. The constant or fixed number is called the common difference. To find the common difference in the arithmetic sequence, subtract any of the two consecutive terms. Keep in mind that you have to add if the arithmetic sequence is arranged in increasing order and subtract if it is in decreasing order.
Let us now find the next three terms in the arithmetic sequences and identify the rules in finding such terms.
A. 5, 10, 15, 20, 25, 30, 35
Rule: Add 5
Common Difference: 25 - 20 = 5
The arithmetic sequence is arranged in increasing order so to find the next terms, add 5 to the previous term.
20 + 5 = 25
25 + 5 = 30
30 + 5 = 35
B. 3, 5, 7, 9, 11, 13, 15
Rule: Add 2
Common Difference: 9 - 7 = 2
The arithmetic sequence is arranged in increasing order so to find the next terms, add 2 to the previous term.
9 + 2 = 11
11 + 2 = 13
13 + 2 = 15
C. 12, 13, 14, 15, 16, 17, 18
Rule: Add 1
Common Difference: 15 - 14 = 1
Add 1 to the previous term.
15 + 1 = 16
16 + 1 = 17
17 + 1 = 18
D. -2, -4, -6, -8, -10, -12
Rule: Add -2
Common Difference: -6 - (-4) = -6 + 4 = -2
Add -2 to the previous term.
-6 + -2 = -8
-8 + -2 = -10
-10 + -2 = -12
E. 128, 428, 928, 1628, 2528, 3628
Rule: Add 700, then add 900 and 1100 or
Add 200 to the previous difference and add the number to the previous term
This case is different from the rest. For this one, you have to find the second difference by finding the differences of the consecutive terms. Then, subtract their differences.
428 - 128 = 300
928 - 428 = 500
Second Difference: 500 - 300 = 200
Since the second difference is 200, you have to keep on adding 200 from the previous difference and add it to the previous term in the sequence.
500 + 200 = 700
928 + 700 = 1628
700 + 200 = 900
1628 + 900 = 2528
900 + 200 = 1100
2528 + 1100 = 3628
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maraming klase ng sequence eh..
Arithmetic Sequence
Geometric Sequence
Harmonic Sequence
Fibonacci Sequence
Split-Exact Sequence
give me a sequence. i'll answer it..
make sure to brainliest this answer so I can see your nest question :)