SOLUTION: The 17th term of an arithmetic progression is 81 and the 33th term is 145. Find a and d a=first term d=common difference

Question 514934: The 17th term of an arithmetic progression is 81 and the 33th term is 145. Find a and d
a=first term
d=common difference
Answer by plover(15) (Show Source): You can put this solution on YOUR website!
From the data
let the seventeenth number be x and the 33rd number in the AP be y
x=a+(n-1)d
x=a+(17-1)d (since it is given n=17)
x=a+16d
81=a+16d (1) (given 17th term is 81)
Also
y=a+(33-1)d
y=a+32d
145=a +32d (2) (given 33rd term is 145)
(1)-(2)
81-145=-16d
-64=-16d
d=4
From 1
81=a+16d
a=81-16*4
=81-64
=17
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