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Show how to work out the following sequences problems.

a.    Consider the sequence:           30 ; 22 ; 14 ; . . .

Find the sum of the first 19 terms of the sequence.

b.    The 5th term of an arithmetic sequence is 17 and a common difference of 6, determine the first term of the sequence.
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## 1 Answer

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a.    Sn = (n/2)[2a + (n - 1)d]

S19 = (19/2)[2x30 + (19 - 1)(-8)]

= (19/2)[60 + (18)(-8)]

= (19/2)(60 - 144)

= -798

b.    To find T1 given T5, we may subtract d = 6 four times from 17 because T5 = a + 4d, that is,

a = 17 - 6 - 6 - 6 - 6 = -7            or T5 = a + 4d

17 = a + 4 x 6

17 - 24 = a

a = -7

by Diamond (39,166 points)

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