The 9th term of an AP is equal to 7times , the 2nd term and 12th term exceeds 5times, the 3rd by two. Find the 1st term and the comman difference.
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nth term = a+(n-1)d
9th term = 7(2nd term)
a+(9-1)d = 7[a+(2-1)d]
a+8d = 7a+7d
d = 8a
12th term -5(3rd term) = 2
a+(12-1)d - 5[a+(3-1)d] = 2
a+11d - 5(a+2d) = 2
a+11d - 5a-10d = 2
-4a -d = 2
-4a -(8a) = 2
-12a = 2
a = -1/6
d = 8a = 8 × -1/6 = -4/3
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