How do you write the first five terms of the arithmetic sequence given #a_1=5, d=6#?

1 Answer
Sep 24, 2017

Answer:

See a solution process below:

Explanation:

The arithmetic sequence formula is:

#a_n = a_1 + (n – 1)d# Where:

#a_n# is the nth term in the sequence

#a_1# is the first term in the sequence

#n# is the term you are solving for

#d# is the common difference for any pair of consecutive numbers in the sequence.

First Term or #n = 1#:

This is given in the problem.

#a_1 = 5#

Second Term or #n = 2#:

Substitute #2# for #n# in the formula and substitute the values from the problem giving:

#a_2 = 5 + ((2 – 1) xx 6)#

#a_2 = 5 + (1 xx 6)#

#a_2 = 5 + 6#

#a_2 = 11#

Fifth Term or #n = 5#:

Substitute #5# for #n# in the formula and substitute the values from the problem giving:

#a_5 = 5 + ((5 – 1) xx 6)#

#a_5 = 5 + (4 xx 6)#

#a_2 = 5 + 24#

#a_2 = 29#

Using this same process you should be able to determiner the
Third Term or #n = 3#: and Fourth Term or #n = 4#: