SOLUTION: solve the arithmetic sequence a5=-2 and a13=30

Question 40979: solve the arithmetic sequence
a5=-2 and a13=30
Answer by psbhowmick(878) (Show Source): You can put this solution on YOUR website!
Let first term = a, common difference = d.
Then an = a + (n-1)d
When n = 6, a6 = -2 = a + 5d
When n = 13, a13 = 30 = a + 12d
Thus we have two equations
a + 5d = -2 ________(1)
a + 12d = 30________(2)
Subtracting eqn. (1) from eqn. (2)
12d - 5d = 30 - (-2)
or 7d = 32
or d = 32/7
So from (1) a = -2 - 5d = -2 - 5(32/7) = -146/7
The series has first term -146/7 and common difference 32/7
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