The first three term of a sequence are given: 2,8,14. Find the 35th term?

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Answer 1 · 2018-02-27T14:02:44

#206# is the #35#th term.

This is an arithmetic sequence, where #d# is the common difference between two consecutive items.

Generally, the #n#th term, #a_n#, of an arithmetic series is given by:

#a_n=a_1+(n-1)d#

Here, #a_1=2#, the first term, and #d=6#. We can input these two values into the general equation:

#a_n=2+6(n-1)#

#a_n=2+6n-6#

#a_n=6n-4#

This is the formula for this sequence. We can use the general equation, but this works too, and it is simpler. Inputting #n=35#, we get:

#a_35=6*35-4#

#a_35=210-4#

#a_35=206#