How do you write a rule for the nth term of the arithmetic sequence and then find #a_22# given #-12, -5, 2, 9...#?

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Answer 1 · 2018-03-17T08:25:38

#color(green)(a_22 )= a_1 + (22-1) * d = -12 + (21 * 7) = color(green)(135#

#a_1 = -12#

#a_2 = -5#

#a_2 - a_1 = -5 - (-12) = -5 + 12 = 7#

#a_3 - a_2 = 2 - (-5) = 2 + 5 = 7#

#a_4 - a_3 = 9 - 2 = 7#

Note common difference #d = a_4 - a_3 = a_3 - a_2 = a_2 - a_1 = 7#

#a_3 = a_2 + d = a_1 + d + d = a_1 + 2d = a_1 + (3-1) * d#

Similarly, #a_4 = a_3 + d = a_1 + 2d + d = a_1 + (4-1) * d#

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

Hence #a_22 = a_1 + (22-1) * d = -12 + (21 * 7) = 135#