Question 141049
write the first five terms of the sequence defined by the given recursive or explicit formula. 

t<sub>n</sub>=32-8n

<pre><font size = 4 color = "indigo"><b>

This is an explicit formula because it does not have t<sub>n</sub> on
one side and t<sub>n+1</sub> or t<sub>n-1</sub> on the other, and
it does not give separately the value of the first term.

t<sub>n</sub>=32-8n

To find the first term, t<sub>1</sub>, we substitute 1 for n

t<sub>n</sub>=32-8n

t<sub>1</sub>=32-8(1)

t<sub>1</sub>=32-8 

t<sub>1</sub>=24

To find the second term, t<sub>2</sub>, we substitute 2 for n

t<sub>n</sub>=32-8n

t<sub>2</sub>=32-8(2)

t<sub>2</sub>=32-16 

t<sub>2</sub>=16

To find the third term, t<sub>3</sub>, we substitute 3 for n

t<sub>n</sub>=32-8n

t<sub>3</sub>=32-8(3)

t<sub>3</sub>=32-24 

t<sub>3</sub>=8

To find the fourth term, t<sub>4</sub>, we substitute 4 for n

t<sub>n</sub>=32-8n

t<sub>4</sub>=32-8(4)

t<sub>4</sub>=32-32 

t<sub>4</sub>=0

To find the fifth term, t<sub>5</sub>, we substitute 5 for n

t<sub>n</sub>=32-8n

t<sub>5</sub>=32-8(5)

t<sub>5</sub>=32-40 

t<sub>5</sub>=-8

So the 5 terms of the sequence are 24, 16, 8, 0, -8 

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You didn't ask this, but you'll need to know it:

The same sequence could have been given to you 
recursively as:

t<sub>n+1</sub> = t<sub>n</sub>-8, t<sub>1</sub> = 24

Notice that it has t's on both sides of the equation and
the first term t<sub>1</sub> is given.

Then we would substitute 2 for n and 24 for t<sub>1</sub> to find t<sub>2</sub>

t<sub>n+1</sub> = t<sub>n</sub>-8
t<sub>1+1</sub> = t<sub>1</sub>-8
t<sub>2</sub> = t<sub>1</sub>-8
t<sub>2</sub> = 24-8
t<sub>2</sub> = 16

Then we would substitute 3 for n and 16 for t<sub>2</sub> to find t<sub>3</sub>

t<sub>n+1</sub> = t<sub>n</sub>-8
t<sub>2+1</sub> = t<sub>2</sub>-8
t<sub>3</sub> = t<sub>2</sub>-8
t<sub>3</sub> = 16-8
t<sub>3</sub> = 8

Then we would substitute 4 for n and 8 for t<sub>3</sub> to find t<sub>4</sub>

t<sub>n+1</sub> = t<sub>n</sub>-8
t<sub>3+1</sub> = t<sub>3</sub>-8
t<sub>4</sub> = t<sub>3</sub>-8
t<sub>4</sub> = 8-8
t<sub>4</sub> = 0

Then we would substitute 5 for n and 0 for t<sub>4</sub> to find t<sub>5</sub>

t<sub>n+1</sub> = t<sub>n</sub>-8
t<sub>4+1</sub> = t<sub>4</sub>-8
t<sub>5</sub> = t<sub>4</sub>-8
t<sub>5</sub> = 0-8
t<sub>5</sub> = -8

So the 5 terms of the sequence are 24, 16, 8, 0, -8 

Edwin</pre>