Question

The 9th term and the 21st term of an AP are 75 and 183 respectively.find 81st term of the AP

Answer 1

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Answer 2

let 9th term be t9 & 21st term be t21 .
tn = a+(n-1)d
t9 = a+(9-1)d
75=a+8d ----(1)
t21 = a+(21-1)d
183 = a+20d ------(2)
substracting eq(1) & (2)
we get , 12d=108
d=108/12
d=9
substituting value of d in eq(1)
75=a+8×9
75=a+72
a=75-72
a=3
therefore t81 (81st term ) is
t81=a+(81-1)d
t81= 3+80×9
t81=3+720
t81 = 723
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