How do you write the first five terms of the arithmetic sequence given #a_1=15, a_(k+1)=a_k+4# and find the common difference and write the nth term of the sequence as a function of n?

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Answer 1 · 2017-12-30T22:02:14

#15, 19, 23, 27, 31#; common difference #d = 4#

#a_n = 15 +4(n-1)#

Given: #a_1 = 15, a_(k+1) = a_k + 4#

Arithmetic sequence has the form: #a_n = a_1 + (n-1)d#,

where #d# is the common difference.

Let #k = 1: " "a_2 = a_1 + 4 = 15 + 4 = 19#

Let #k = 2: " "a_3 = a_2 + 4 = 19 + 4 = 23#

Let #k = 3: " "a_4 = a_3 + 4 = 23 + 4 = 27#

Let #k = 4: " "a_5 = a_4 + 4 = 27 + 4 = 31#

First five terms of the arithmetic sequence: #15, 19, 23, 27, 31#

common difference: #d = 19-15 = 23-19 = 27-23 = 4#

#a_n = a_1 + (n-1)d = 15 + 4(n-1)#