1. Arithmetic Sequence
Determines arithmetic means, nth term of an arithmetic
sequence and sum of the terms of a given arithmetic
sequence. (M10AL-Ib-1)
NATANIEL B. SANTOS JR.
2. What is ARITHMETIC SEQUENCE
• A sequence is a function whose domain is the finite set {1, 2, 3,…, n} or the
infinite set {1, 2, 3,… }.
• An arithmetic sequence is a sequence where every term after the first is
obtained by adding a constant called the common difference.
Example: 1, 4, 7, 10, 13 finite
15, 11, 7, 3, -1, … infinite
7. 1. What is the 10th
term in the arithmetic
sequence 5, 12, 19, 26, … ?
• 5, 12, 19, 26, 33, 40, 47, 54, 61, 68
• How about the 20th
term?
• How about the 105th
term?
• How about the 1000th
term?
1st 2nd 7th 8th 9th 10th
4th 5th 6th
3rd
12. Seatwork # 104: Answer each of the following.
1. What is the 8th
term in the arithmetic sequence -5, -7, -9, -11, …?
2. What is the 13th
term in the arithmetic sequence 82, 73, 64, 55, 46, … ?
3. What is the 28th
term in the arithmetic sequence 1, 14, 27, 40, 53, 66, … ?
4. What is the 50th
term in the arithmetic sequence -99, -94, -89, -84, -79, … ?
5. What is the 102nd
term in the arithmetic sequence – 10, -20, -30, -40, … ?
13. If the 5th term of an arithmetic sequence is 23 and
the common difference is 4, what is the 10th term?
• 23
• n = 5
14. If the 5th term of an arithmetic sequence is 23 and
the common difference is 4, what is the 10th term?
• 23
• 23
• 23
• 23-16
15. If the 5th term of an arithmetic sequence is 23 and
the common difference is 4, what is the 10th term?
• n = 10
16. If the 5th term of an arithmetic sequence is 23 and
the common difference is 4, what is the 10th term?
17. More examples:
• 1. If the 9th term of an arithmetic sequence is 20 and the common
difference is -5, what is the 18th term?
• 2. If the 7th term of an arithmetic sequence is -28 and the common
difference is 4, what is the 23rd term?
18. Seatwork # 105
1. If the 4th term of an arithmetic sequence is -10 and the common
difference is -2, what is the 11th term?
2. If the 6th term of an arithmetic sequence is 70 and the common difference
is -5, what is the 20th term?
3. If the 5ht term od an arithmetic sequence is -4 and the common difference
is 11, what is the 32nd term?
19. Arithmetic Means are the terms between any two
nonconsecutive terms of an arithmetic sequence.
• Insert 4 arithmetic means between 5 and 25.
• Since we are required to insert 4 terms, then there will be 6 terms
in all.
• 5, ___, ___, ___, ___, 25
20. Arithmetic Means are the terms between any two
nonconsecutive terms of an arithmetic sequence.
• Common difference:
21. Arithmetic Means are the terms between any two
nonconsecutive terms of an arithmetic sequence.
• 25
• 25
• 25
• 20
• 4
22. Arithmetic Means are the terms between any two
nonconsecutive terms of an arithmetic sequence.
• 5, ___, ___, ___, ___, 25
• 5+4=9 9+4=13
• 13+4=17 17+4=21
9 13 17 21
23. More examples:
1. Insert 5 arithmetic means between 2 and 38.
2. Insert 3 arithmetic means between -55 and -11
3. Insert 8 arithmetic means between -6 and -51
24. Seatwork #106: Solve for the arithmetic means
in each of the following.
1. Insert 4 arithmetic means between 7 and 27
2. Insert 5 arithmetic means between 62 and 8
3. Insert 7 arithmetic means between -100 and -20
4. Insert 10 arithmetic means between -9 and -42
5. Insert 8 arithmetic means between 32 and -13
25. What is the sum of the first 10 terms in 8, 12,
16, 20, 24, … ?
• 8, 12, 16, 20, 24, ___, ___, ___, ___, ___,
• =8+12+16+20+24+28+32+36+40+44
• =260
• What about first 15 terms?
• What about first 100 terms?
• What about first 3000 terms?
28 32 36 40 44
27. Find the sum of the first 10 terms of the
arithmetic sequence 5, 9, 13, 17, ...
28. More Examples:
1. Find the sum of the first 20 terms of the arithmetic sequence -2, -5, -8, -11,
…
2. What is the sum of the first 15 terms in the arithmetic sequence 7, 13, 19,
25, 31, …?
3. Find the sum of the first 18 terms of the arithmetic sequence 78, 69, 60,
51, 42, …?
29. Seatwork #107: Find the sum of terms in each
of the following.
1. Find the sum of the first 10 terms of the arithmetic sequence 15, 22, 29, 36, …
2. What is the sum of the first 15 terms in the arithmetic sequence -3,-11,-19, -27, -35,
…?
3. Find the sum of the first 20 terms of the arithmetic sequence -85, -74, -63, -52, -41,
…?
4. Find the sum of the first 18 terms of the arithmetic sequence -3, -13, -23, -33, -43,
…?
5. What is the sum of the first 27 terms in the arithmetic sequence 103, 95, 87, 79, 71,
…?
