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t(n) = a + 8*d = 54 .. .. .. .. .. .. .. (A)

s(12) = 12*a + 66*d = 438 .. .. .. .. (B)

12*(A) - (B) => 12*A + 96*d -12*A - 66*D = 648 - 438

=> 30*d = 210 = d = 7

Then substituting this value in (A) gives a + 54 = 54 => a = -2

So the first term is -2 and the common difference is 7.

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Q: The ninth term of an arithmetic progression is 54 and the sum of the 12 terms 438 find the first term and the common difference?
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