What is the 40th term of the sequence 14, 9, 4, -1?

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Answer 1 · 2016-12-18T17:15:16

#40#th term: #s = -181#

#s_2(9) = s_1(14)-5#

#s_3(4) = s_2(9)-5#

to find the first part of the #n#th term, you take what happens to one term as it passes to the next and apply that to #n#.

first part: #-5n#

however, #-5 * 1# is not equal to #s_1(14)#, so the term is changed accordingly.

#14 = (-5 * 1) + 19#

the #n#th term becomes #-5n + 19#.

#40#th term: #n = 40#

#(-5 * 40) + 19 = -200 + 19#

#= -181#

#40#th term: #s = -181#