Determine the indicated term in the following arithmetic sequences. 1.) a subscript 5: {2, 5, 8, ...}

2.) a subscript 20: {4, 8, 12, ...}

3.) a subscript 18: {0,20,40,60, ...}

Skip to content# Determine the indicated term in the following arithmetic sequences.1.) a subscript 5: {2, 5, 8, …}2.) a subscript 20: {4, 8, 12, …}3.)

Mathematics ##
Comments (3) on “Determine the indicated term in the following arithmetic sequences.1.) a subscript 5: {2, 5, 8, …}2.) a subscript 20: {4, 8, 12, …}3.)”

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2.) a subscript 20: {4, 8, 12, ...}

3.) a subscript 18: {0,20,40,60, ...}

[tex]a_5= 14[/tex]

[tex]a_{20}= 80[/tex]

[tex]a_{18}= 340[/tex]

Step-by-step explanation:

Solving (a):

We have:

[tex]a_1=2[/tex] --- first term

[tex]d = 5 -2 = 3[/tex] common difference

The 5h term is:

[tex]a_n= a_1 + (n - 1)d[/tex]

[tex]a_5= 2+ (5 - 1)*3[/tex]

[tex]a_5= 14[/tex]

Solving (b):

We have:

[tex]a_1 = 4[/tex] --- first term

[tex]d = 8 -4 = 4[/tex] common difference

The 20h term is:

[tex]a_n= a_1 + (n - 1)d[/tex]

[tex]a_{20}= 4+ (20 - 1)*4[/tex]

[tex]a_{20}= 80[/tex]

Solving (c):

We have:

[tex]a_1 = 0[/tex] --- first term

[tex]d = 20 -0 = 20[/tex] common difference

The 18th term is:

[tex]a_n= a_1 + (n - 1)d[/tex]

[tex]a_{18}= 0+ (18 - 1)*20[/tex]

[tex]a_{18}= 340[/tex]

6(2x + 5y)6 (2x) = 12x6 (5y) = 30y12x + 30y

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