The kth term, t(k) is given by t(k) = 2k2 + 2k
So the sum of the first n terms is 2*(12+22+32+...+n2) + 2*(1+2+3+...+n)
= 2*n(n+1)(2n+1)/6 + 2*n(n+1)/2
= n(n+1)*(2n+1)/3 + n(n+1)
= n(n+1)*(2n+1+3)/3
= 2*n(n+1)(n+2)/3
Sum = n/2(2a + (n-1)d) = 11/2 x (2 x -12 + 10 x 5) = 11/2 x 26 = 143
7/12 is another.
The sum of the first five terms of a geometric series can be calculated using the formula ( S_n = a_1 \frac{1 - r^n}{1 - r} ), where ( a_1 ) is the first term, ( r ) is the common ratio, and ( n ) is the number of terms. Here, ( a_1 = 6 ), ( r = 13 ), and ( n = 5 ). Substituting these values into the formula gives: [ S_5 = 6 \frac{1 - 13^5}{1 - 13} = 6 \frac{1 - 371293}{-12} = 6 \cdot \frac{-371292}{-12} = 6 \cdot 30939 = 185634 ] Thus, the sum of the first five terms is 185634.
0.9231
Calculating an average is done in two steps: - First: you calculate the sum of the terms whose average you would like to calculate. - Second: you divide the sum of the terms by their number. In your case: - First: 10 + 6 + 12 = 28 - Second: 28 / 3 = 9.33333.... 3 is the number of terms added together which are: 10, 6 and 12 (3 numbers). Answer: Therefore your average is: 9.33333....
To find the sum of the first 48 terms of an arithmetic sequence, we can use the formula for the sum of an arithmetic series: Sn = n/2 * (a1 + an), where Sn is the sum of the first n terms, a1 is the first term, and an is the nth term. In this case, a1 = 2, n = 48, and an = 2 + (48-1)*2 = 96. Plugging these values into the formula, we get: S48 = 48/2 * (2 + 96) = 24 * 98 = 2352. Therefore, the sum of the first 48 terms of the given arithmetic sequence is 2352.
Sum = n/2(2a + (n-1)d) = 11/2 x (2 x -12 + 10 x 5) = 11/2 x 26 = 143
12(6 + 5)
7/12 is another.
0.9231
-0.86546 and 13.86546 (approx).
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.
The sum of z and 12 can be calculated by adding the value of z to 12. In mathematical terms, the sum of z and 12 is represented as z + 12. This operation involves combining the numerical value of z with 12 to obtain the total sum.
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Eight. (8)
Guys 1/6 3/12 and 5/18
Un = 4*3n-1 S9 = 39364