-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.
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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6
The given sequence is an arithmetic sequence with a common difference that increases by 1 with each term. To find the nth term of an arithmetic sequence, you can use the formula: nth term = a + (n-1)d, where a is the first term, n is the term number, and d is the common difference. In this case, the first term (a) is 3 and the common difference (d) is increasing by 1, so the nth term would be 3 + (n-1)(n-1) = n^2 + 2.
-8
The given sequence 6, 8, 10, 12 is an arithmetic sequence with a common difference of 2 between each term. To find the nth term of an arithmetic sequence, you can use the formula: (a_n = a_1 + (n-1)d), where (a_n) is the nth term, (a_1) is the first term, (n) is the term number, and (d) is the common difference. In this case, the first term (a_1) is 6 and the common difference (d) is 2. So, the nth term (a_n = 6 + (n-1)2 = 2n + 4).
-8
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, ...
To find the sum of all even numbers from 2 through 200, we can use the formula for the sum of an arithmetic series. Since the sequence is an arithmetic sequence with a common difference of 2, we can calculate the number of terms using the formula ((last term - first term) / common difference) + 1. In this case, the first term is 2, the last term is 200, and the common difference is 2. Plugging these values into the formula gives us ((200 - 2) / 2) + 1 = 100. The sum of an arithmetic series is given by the formula n/2 * (first term + last term), so the sum of all even numbers from 2 through 200 is 100/2 * (2 + 200) = 10100.
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