Problema Solution
The sum of the first 13 terms in arithmetic sequence is 1,475.5 while 131 is known to be the 8th
term. Find the first term and common difference of this sequence?
Answer provided by our tutors
Let
a1 = the first term,
an = the last term,
d = the common difference
an = a1 + (n-1)d
a8 = 131
a8 = a1 + (8-1)d
a1 + 7d = 131
S13 = 1475.5
S13 = (13/2)(a1 + a13)
a13 = a1 + 12d
S13 = (13/2)(a1 + a1 + 12d)
S13 = 13(a1 + 6d)
13(a1 + 6d) = 1475.5
We have the system of equations:
a1 + 7d = 131
13(a1 + 6d) = 1475.5
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a1 = 8.5
d = 17.5
The first term is 8.5.
The common difference is 17.5.