2
An arithmetic sequence.
The following formula generalizes this pattern and can be used to find ANY term in an arithmetic sequence. a'n = a'1+ (n-1)d.
It is 58465.
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.
The difference between successive terms in an arithmetic sequence is a constant. Denote this by r. Suppose the first term is a. Then the nth term, of the sequence is given by t(n) = (a-r) + n*r or a + (n-1)*r
It is not possible to answer this question without information on whether the terms are of an arithmetic or geometric (or other) progression, and what the starting term is.
To find the first term of an arithmetic progression (AP), you need at least two pieces of information: the common difference and either the second term or the sum of the first few terms. The first term can be represented as ( a ), and the ( n )-th term can be expressed as ( a_n = a + (n-1)d ), where ( d ) is the common difference. If you know the second term, you can rearrange it to find ( a = a_2 - d ). Without specific values or additional context, the first term cannot be determined.
There are 5 common differences between seventh and twelfth terms, so the CD is 2.5/5 ie 0.5. First term is therefore 15 - 6 x 0.5 = 12.
An arithmetic sequence.
Multiply them together.
To find the sum of the first 20 terms of an arithmetic progression (AP), we need to first determine the common difference (d) between the terms. Given that the 6th term is 35 and the 13th term is 70, we can calculate d by subtracting the 6th term from the 13th term and dividing by the number of terms between them: (70 - 35) / (13 - 6) = 5. The formula to find the sum of the first n terms of an AP is Sn = n/2 [2a + (n-1)d], where a is the first term. Plugging in the values for a (the 1st term), d (common difference), and n (20 terms), we can calculate the sum of the first 20 terms.
The following formula generalizes this pattern and can be used to find ANY term in an arithmetic sequence. a'n = a'1+ (n-1)d.
It is 58465.
The sum of the 1st n terms is : N(3N-1)/2 Explanation : The sum from 1 to N of (3m-2) = 3 * sumFrom1toN(m) - sumFrom1toN(2) = 3 * (N*(N+1)/2) -2*N = N(3N-1)/2 For N=10 => 145
To find the first three terms of an arithmetic sequence with a common difference of -5, we first need the last term. If we denote the last term as ( L ), the terms can be expressed as ( L + 10 ), ( L + 5 ), and ( L ) for the first three terms, since each term is derived by adding the common difference (-5) to the previous term. Thus, the first three terms would be ( L + 10 ), ( L + 5 ), and ( L ).
To find the first arithmetic mean between -15 and 9 with three means inserted, we first calculate the total number of terms, which is 5: -15, A1, A2, A3, and 9. The common difference (d) can be calculated as the difference between the last term and the first term divided by the number of intervals (4). Thus, ( d = \frac{9 - (-15)}{4} = \frac{24}{4} = 6 ). The first arithmetic mean (A1) is then -15 + 6 = -9.
To find the number of terms in the arithmetic sequence given by 1316197073, we first identify the pattern. The sequence appears to consist of single-digit increments: 13, 16, 19, 20, 73. However, this does not follow a consistent arithmetic pattern. If the sequence is intended to be read differently or if there are specific rules governing its formation, please clarify for a more accurate answer.