9514 1404 393
Answer:
(A) -2018
(B) 5/36
Step-by-step explanation:
(A) The rate of change between any pair of terms in an arithmetic sequence is the same:
(a668 -a38)/(668 -38) = (a38 -a13)/(38 -13)
a668/630 = a38/630 +(a38 -a13)/25 . . . . add a38/630 to both sides
a668 = a38 +630/25(a38 -a13) = -128 +25.2(-128 -(-53)) = -128 -1890
a668 = -2018
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(B) The sum of an infinite geometric series is ...
S = a1/(1 -r) . . . . . . for first term a1 and common ratio r
We are given S = 6, a1 = 5, so we can find r to be ...
6 = 5/(1 -r)
1 -r = 5/6
1 -5/6 = r = 1/6
Then the 3rd term is ...
a3 = 5×(1/6)^(3 -1) = 5/36
