Question #85add

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Answer 1 · 2017-09-12T01:17:13

The expression is:

#color(blue)(5n -2)#

This is an arithmetic sequence.

The n term of an arithmetic sequence can be written:

#color(blue)(a) + (n - 1)color(blue)(d)#

Where #color(blue)(a)# is the first term in the sequence and #color(blue)(d)# is the common difference.

The common difference here is #5#

So: #color(blue)(d) = 5#

First term is #3#

So: # color(blue)(a) = 3#

Inputting values:

#3 + (n - 1 )5#

Expanding and collecting terms:

#3 + 5n - 5 => 5n -2#

To check:

The fourth term is:

#5(4) - 2 = 20 - 2 = color(blue)(18)#