SOLUTION: In an arithmetic sequence, t23 = 519 and t71 = 1503, what is t114

Question 939630: In an arithmetic sequence, t23 = 519 and t71 = 1503, what is t114
Answer by laoman(51) (Show Source): You can put this solution on YOUR website!
For an aritmetic sequence, tn= a+(n-1)*d
Where a is the first term, n is the no. of terms and d is the common difference,
Given t23 = a+22d=519 and t71 = a+70d=1503
To find t114 = a+113d
Let's find the values of a and d using the simultaneous equations above
We have,
a+22d=519
a+70d=1503
Subtracting the second equation from the first,
a-a+22d-70d=519-1503
-48d = -984
d = -984/-48 = 20.5
d =20.5
From the first eqn, a +22d = 519
a=519-22*d=519-22*20.5=519-451
a=68
Now we know a=68 and d=20.5
t114 = a+113d =68+113*20.5 = 68+2316.5
t114=2384.5
QED
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