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-8
-8
36
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.
Oh, dude, it's like a pattern party! So, to find the nth term for this sequence, you first need to figure out the pattern. Looks like each number is decreasing by 2. So, the nth term would be 13 - 2n. Easy peasy, right?