Answer:

SEQUENCES

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\large \bold{\blue{PROBLEM:}}PROBLEM: What are the next 5 terms of the geometric sequence if the first term is 4 and the ratio is 3?

\large \bold{\blue{SOLUTION:}}SOLUTION: The next 5 terms of the sequence would be \sf a_2,a

2

, \sf a_3,a

3

, \sf a_4,a

4

, \sf a_5,a

5

, and \sf a_6a

6

since the first term is already given. Use the geometric sequence formula then apply it to each nth term.

\boxed{a_n = a_1 \cdot r^{n-1}}

a

n

=a

1

⋅r

n−1

• Find \sf a_2a

2

:

a_2 = 4 \cdot 3^{2-1}a

2

=4⋅3

2−1

a_2 = 4 \cdot 3^1a

2

=4⋅3

1

a_2 = 4 \cdot 3a

2

=4⋅3

a_2 = 12a

2

=12

• Find \sf a_3a

3

:

a_3 = 4 \cdot 3^{3-1}a

3

=4⋅3

3−1

a_3 = 4 \cdot 3^2a

3

=4⋅3

2

a_3 = 4 \cdot 9a

3

=4⋅9

a_3 = 36a

3

=36

• Find \sf a_4a

4

:

a_4 = 4 \cdot 3^{4-1}a

4

=4⋅3

4−1

a_4 = 4 \cdot 3^3a

4

=4⋅3

3

a_4 = 4 \cdot 27a

4

=4⋅27

a_4 = 108a

4

=108

• Find \sf a_5a

5

:

a_5 = 4 \cdot 3^{5-1}a

5

=4⋅3

5−1

a_5 = 4 \cdot 3^4a

5

=4⋅3

4

a_5 = 4 \cdot 81a

5

=4⋅81

a_5 = 324a

5

=324

• Find \sf a_6a

6

:

a_6 = 4 \cdot 3^{6-1}a

6

=4⋅3

6−1

a_6 = 4 \cdot 3^5a

6

=4⋅3

5

a_6 = 4 \cdot 243a

6

=4⋅243

a_6 = 972a

6

=972

» Thus, the next 5 terms of the geometric sequence are:

\large \underline{\boxed{\tt \purple{12, \, 36, \, 108, \, 324, \, and \: 972}}}

12,36,108,324,and972

Answer:

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