<PRE><B>Question 1136793</B>
the formula for the nth term of an arithmetic sequence is
:
a(n) = a(0) +d(n-1), where a(0) is the first term and d is the common difference
:
we are given two equations in two unknowns
:
a(9) = -8 = a(0) +d(9-1)
:
1) a(0) +8d = -8
:
a(17) = 32 = a(0) +d(17-1)
:
2) a(0) +16d = 32
:
solve equation 1 for a
:
a(0) = -8 -8d
:
substitute for a(0) in equation 2
:
(-8 -8d) +16d = 32
:
8d = 40
:
d = 5
:
a(0) = -8 -8(5)
:
a(0) = -48
:
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the first term is -48
:
the recursive rule is
:
a(0) = -48, a(n) = a(n-1) +5
:
check the answer
:
For equation 1
:
a(9) = -48 +8(5) = -8
:
-8 = -8
:
For equation 2
:
a(17) = -48 +16(5) = 32
:
32 = 32
:
answer checks
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