Answer:

✏️SEQUENCES

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Exercise 1

A. Directions: Identify the first term and find the common difference of each arithmetic sequence.

#1: 5, 10, 15, 20, 25, 30, ...

First term: \large \tt \green{5}5

Common difference (d): \large \tt \green{5}5

#2: 34, 27, 20, 13, 6, -1, -8, ...

First term: \large \tt \green{34}34

Common difference (d): \large \tt \green{\text-7}-7

\:

B. Directions: Find the next term of the given arithmetic sequence.

#1: 3, 10, 17, 24, 31, \large \underline{\tt \green{\,38\,}}

38

#2: 3, 13, 23, 33, 43, \large \underline{\tt \green{\,53\,}}

53

#3: 25, 20, 15, 10, 5, 0, \large \underline{\tt \green{\,\text-5\,}}

-5

, -10

\:

C. Assessment / Application

• Find the first term and common difference of each arithmetic sequence.

#1: \large \underline{\tt \green{\,15\,}}

15

, 20, 25, 30, 35, 40, ... \large \tt \green{d = 5}d=5

#2: \large \underline{\tt \green{\,34\,}}

34

, 31, 28, 25, 22, 19, 16, ... \large \tt \green{d = \text-3 }d=-3

#3: \large \underline{\tt \green{\,10\,}}

10

, 13, 16, 19, 22, 25, ... \large \tt \green{d = 3}d=3

#4: \large \underline{\tt \green{\,0\,}}

0

, 12, 24, 36, 48, 60, ... \large \tt \green{d = 12}d=12

\:

• Find the next term/s of the given sequence.

#1: 3, 10, 17, 24, 31, 38, \large \underline{\tt \green{\,45\,}}

45

, ...

#2: -10, -12. -14, -16, \large \underline{\tt \green{\,\text-18\,}}

-18

, \large \underline{\tt \green{\,\text-20\,}}

-20

, -22, ...

#3: 8, 15, 22, 29, 36, \large \underline{\tt \green{\,43\,}}

43

, \large \underline{\tt \green{\,50\,}}

50

, 57, ...

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Exercise 2

» Write the first six terms of a sequence described by the general term:

\boxed{a_n = 4n + 1}

a

n

=4n+1

• Identify the first term \sf (a_1)(a

1

)

a_1 = 4(1) + 1a

1

=4(1)+1

a_1 = 4 + 1a

1

=4+1

a_1 = 5a

1

=5

• Identify the second term \sf (a_2)(a

2

)

a_2 = 4(2) + 1a

2

=4(2)+1

a_2 = 8 + 1a

2

=8+1

a_2 = 9a

2

=9

• Identify the third term \sf (a_3)(a

3

)

a_3 = 4(3) + 1a

3

=4(3)+1

a_3 = 12 + 1a

3

=12+1

a_3 = 13a

3

=13

• Identify the fourth term \sf (a_4)(a

4

)

a_4 = 4(4) + 1a

4

=4(4)+1

a_4 = 16 + 1a

4

=16+1

a_4 = 17a

4

=17

• Identify the fifth term \sf (a_5)(a

5

)

a_5 = 4(5) + 1a

5

=4(5)+1

a_5 = 20 + 1a

5

=20+1

a_5 = 21a

5

=21

• Identify the sixth term \sf (a_6)(a

6

)

a_6 = 4(6) + 1a

6

=4(6)+1

a_6 = 24 + 1a

6

=24+1

a_6 = 25a

6

=25

» Thus, the first 6 terms of the sequence are:

\large \underline{\boxed{\tt \purple{5, 9, 13, 17, 21, and \: 25}}}

5,9,13,17,21,and25