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What formula represents the partial sum of the first n terms of the series 5 10 15 20 25?
The series given is an arithmetic progression consisting of 5 terms with a common difference of 5 and first term 5 → sum{n} = (n/2)(2×5 + (n - 1)×5) = n(5n + 5)/2 = 5n(n + 1)/2 As no terms have been given beyond the 5th term, and the series is not stated to be an arithmetic progression, the above formula only holds for n = 1, 2, ..., 5.
What is the sum of the first 15 multiples of 8?
Sum of the first 15 positive integers is 15*(15+1)/2 = 120 Sum of the first 15 multiples of 8 is 8*120 = 960
The fourth term of an AP is 15 and the sum of the first 5 terms is 55. Find the first term and the common difference?
x is the first term and d is the difference then x + 3d = 15 and sum of first five terms isx + (x+d) + (x+2d) + (x+3d) + (x+4d)so 5x + 10d = 55 ie x + 2d = 11As x + 3d = 15, d = 4 and x = 3,giving the five terms as 3, 7, 11, 15 and 19
What is the sum of the first fifteen odd numbers?
The sum of the first 15 odd numbers is 225.
What is the sum of the first five whole numbers?
The sum of the first five whole numbers is 10.
What is the sum of the arithmetic sequence from 3 to 90 which are divisible by 5?
To find the sum of the arithmetic sequence from 3 to 90 that is divisible by 5, we first identify the terms: the first term is 5 and the last term is 90. The sequence of terms divisible by 5 is 5, 10, 15, ..., 90. This is an arithmetic sequence where the first term (a = 5), the last term (l = 90), and the common difference (d = 5). The number of terms (n) can be calculated as ((l - a)/d + 1 = (90 - 5)/5 + 1 = 18). The sum (S_n) of the sequence can be calculated using the formula (S_n = n/2 \times (a + l)), resulting in (S_{18} = 18/2 \times (5 + 90) = 9 \times 95 = 855). Thus, the sum is 855.
What is the definition for the mathematical term mean?
The arithmetic mean is an average arrived at by adding all the terms together and then dividing by the number of terms. Example : Add the digits up and then divide the sum by the number of separate numbers. For the numbers 2, 4, and 9, the sum is 15 and the mean is 15/3 or 5.
What is the sum of first 15 multiples of 6?
6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72, 78, 84, 90.
If three arithmetic means are inserted between -15 and 9 find the first of these arithmetic means..?
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.
What formula represents the partial sum of the first n terms of the series 5 10 15 20 25?
The series given is an arithmetic progression consisting of 5 terms with a common difference of 5 and first term 5 → sum{n} = (n/2)(2×5 + (n - 1)×5) = n(5n + 5)/2 = 5n(n + 1)/2 As no terms have been given beyond the 5th term, and the series is not stated to be an arithmetic progression, the above formula only holds for n = 1, 2, ..., 5.
What is the sum of the first 15 multiples of 8?
Sum of the first 15 positive integers is 15*(15+1)/2 = 120 Sum of the first 15 multiples of 8 is 8*120 = 960
Is 15 26 37 48 59 an arithmetic sequence?
It is an Arithmetic Progression with a constant difference of 11 and first term 15.
What is the sum of the first 15 prime numbers?
the sum of the first 15 prime numbers is 328 .
What is the sum of the geometric sequence 8comma negative16comma 32 dot dot dot if there are 15 terms?
The sum of a geometric sequence is a(1-rn)/(1-r) In this case, a = 8, r = -2 and n=15 So the sum is 8(1-(-2)15)/(1+2) =8(1+32768)/3 =87,384 So the sum of the first 15 terms of the sequence 8, -16, 32, -64.... is 87,384.
The fourth term of an AP is 15 and the sum of the first 5 terms is 55. Find the first term and the common difference?
x is the first term and d is the difference then x + 3d = 15 and sum of first five terms isx + (x+d) + (x+2d) + (x+3d) + (x+4d)so 5x + 10d = 55 ie x + 2d = 11As x + 3d = 15, d = 4 and x = 3,giving the five terms as 3, 7, 11, 15 and 19
What is first term of a geometric series is 3 and the sum of the first term and the second term is 15 What is the sum of the first six terms?
In a geometric series, if the first term ( a ) is 3 and the sum of the first and second terms is 15, we can denote the common ratio as ( r ). Therefore, we have ( 3 + 3r = 15 ), which simplifies to ( 3r = 12 ) or ( r = 4 ). The sum of the first six terms can be calculated using the formula ( S_n = a \frac{1 - r^n}{1 - r} ). Substituting ( a = 3 ), ( r = 4 ), and ( n = 6 ), we get ( S_6 = 3 \frac{1 - 4^6}{1 - 4} = 3 \frac{1 - 4096}{-3} = 4095 ).
What is the sum of the first 15 whole numbers?
The sum of the smallest 15 positive integers is 120. The sum of the smallest 15 negative integers is -120.
