How do you write the expression for the nth term of the sequence given #1, 4, 7, 10, 13,...#?

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Answer 1 · 2017-02-27T07:16:06

#:. "nth term" = 1+(n-1)*3 #

#1;4;7;10;13;...........# is an arithmetic series

#n_1=1 # and the common difference, #d=3#

#:. " nth term" = 1+(n-1)*3 "#

Answer 2 · 2017-03-10T15:30:22

#T_n = 3n -2# is the expression for any term in the given sequence.

We should recognise that #1, 4, 7, 10, 13 ....# is an A.P. with a common difference of 3.

#d = 3#

The expression for the nth term can be determined from the formula, but there is a short cut.

#T_n = d xx n + ???#

As soon as see that #d = 3#, you will know that the expression for the nth term with start with #T_n = 3n#

Now you just have find what must be added or subtracted to start at the correct first term.

Let #n=1" "rarr 3 xx 1 = 3," but " T_1# must be #1,# so subtract 2

Let #n=2" "rarr 3 xx 2= 6" but " T_2# must be #4. # so subtract 2

It would seem that the expression we want is: #T_n = 3n -2#

Check with #T_3# which must be 7.

#3 xx 3 - 2 =7#

#T_n = 3n -2#

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Using the formula : #T_n = a + (n-1)d#

In #1, 4, 7, 10, 14, ...#

#a = T_1 = 1" and "d = 3#

#T_n = 1 + (n-1)xx3" "larr# simplify

#T_n = 1+3n -3#

#T_n = 3n -2#