What is the 32nd term of the arithmetic sequence where a1 = 14 and a13 = -58?

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Answer 1 · 2015-07-17T22:46:00

The 32nd term of the sequence is #color(red)(-172)#.

We know that #a_1 = 14# and #a_13 = -58#.

We can use the #n^"th"# term rule for an arithmetic sequence:

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

#a_13 = a_1 + (13-1)d#

#-58 = 14 + 12d#

#-58 -14 = 12d#

#-72 = 12d#

#d = -72/12#

#d = -6#

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

#a_32 = 14 +(32-1)(-6) = 14 +31(-6) = 14-186#

#a_32 = -172#