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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.
The nth term of a arithmetic sequence is given by: a{n} = a{1} + (n - 1)d → a{5} = a{1} + (5 - 1) × 3 → a{5} = 4 + 4 × 3 = 16.
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Placing a question mark at the end of some phrases does not make it a sensible question.
If the first term, t(1) = a and the common difference is r then t(n) = a + (n-1)*r where n = 1, 2, 3, ...
n = 1, 2n = 2 n = 2, 2n = 4 n = 3, 2n = 6 2, 4, 6, ..., 2n where n = 1, 2, 3, ... This is an arithmetic sequence, where the first term is 2 and the common difference is 2.
Since there are no graphs following, the answer is none of them.
sum = 1/2 x number_of_terms x (first + last) number_of_terms = (last - first) ÷ difference + 1 = (25 - 0.5) ÷ 3.5 + 1 = 8 ⇒ sum = 1/2 x 8 x (0.5 + 25) = 102
The sum of the first 12 terms of an arithmetic sequence is: sum = (n/2)(2a + (n - 1)d) = (12/2)(2a + (12 - 1)d) = 6(2a + 11d) = 12a + 66d where a is the first term and d is the common difference.
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Find the 7th term of the geometric sequence whose common ratio is 1/2 and whose first turn is 5