How do you find an equation that describes the sequence #14, 15, 16, 17,...# and find the 16th term?

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Answer 1 · 2018-03-17T10:03:37

#color(red)(a_16 = 29#

Given : #a_1 = 14, a_2 = 15, a_3 = 16, a_4 = 17#

To find the #16^(th)# term.

We know, common difference #d = a_2 - a_1 = a_3 - a_2 = a_4 - a_3#

#d = 15 - 14 = 16 - 15 = 17 - 16 = 1#

#n^(th)# term of an Arithmetic Sequence is given by the formula,

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

#a_16 = 14 + (16-1) * 1 = 14 + 15 = 29#