SOLUTION: When given t2=4 and t5=22, how would you find t23 in a arithmetic sequence?

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Question 745180: When given t2=4 and t5=22, how would you find t23 in a arithmetic sequence?
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
t2 = 4

t3 = t2+d

t3 = 4+d

t4 = t3 + d

t4 = (4+d) + d

t4 = 4 + 2d

t5 = t4 + d

t5 = (4+2d) + d

t5 = 4 + 3d

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t5 = 4 + 3d

22 = 4 + 3d

22 - 4 = 3d

18 = 3d

3d = 18

d = 18/3

d = 6

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t1 = t2 - d

t1 = 4 - 6

t1 = -2

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tn = t1 + d(n-1)

tn = -2 + 6(n-1)

tn = -2 + 6n-6

tn = 6n - 8

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tn = 6n - 8

t23 = 6*23 - 8

t23 = 130