the formula is:
Sn= n [2(A1)+(n - 1)d]
2
for example the given sequence is when A1 = 4 and n = 10 when d = 2 here is the solution:
Sn = 4 [2(4)+(10 - 1)2]
2
Sn= 2 [6+(9)(2)
Sn = 2 [6+18]
Sn = 2 (24)
Sn = 48
see?
an = a1 + d(n - 1)
It is an arithmetic sequence for which the index goes on and on (and on).
To find the sum of the first 28 terms of an arithmetic sequence, you need the first term (a) and the common difference (d). The formula for the sum of the first n terms (S_n) of an arithmetic sequence is S_n = n/2 * (2a + (n - 1)d). Once you have the values of a and d, plug them into the formula along with n = 28 to calculate the sum.
You didn't say the series (I prefer to use the word sequence) of even numbers are consecutive even numbers, or even more generally an arithmetic sequence. If we are not given any information about the sequence other than that each member happens to be even, there is no formula for that other than the fact that you can factor out the 2 from each member and add up the halves, then multiply by 2: 2a + 2b + 2c = 2(a + b + c). If the even numbers are an arithmetic sequence, you can use the formula for the sum of an arithmetic sequence. Similarly if they are a geometric sequence.
That's an arithmetic sequence.
12, 6, 0, -6, ...
an = a1 + d(n - 1)
The answer depends on what the explicit rule is!
origin of arithmetic sequence
It is an arithmetic sequence for which the index goes on and on (and on).
An arithmetic sequence is a list of numbers which follow a rule. A series is the sum of a sequence of numbers.
-7
arithmetic sequence * * * * * A recursive formula can produce arithmetic, geometric or other sequences. For example, for n = 1, 2, 3, ...: u0 = 2, un = un-1 + 5 is an arithmetic sequence. u0 = 2, un = un-1 * 5 is a geometric sequence. u0 = 0, un = un-1 + n is the sequence of triangular numbers. u0 = 0, un = un-1 + n(n+1)/2 is the sequence of perfect squares. u0 = 1, u1 = 1, un+1 = un-1 + un is the Fibonacci sequence.
That's an arithmetic sequence.
You didn't say the series (I prefer to use the word sequence) of even numbers are consecutive even numbers, or even more generally an arithmetic sequence. If we are not given any information about the sequence other than that each member happens to be even, there is no formula for that other than the fact that you can factor out the 2 from each member and add up the halves, then multiply by 2: 2a + 2b + 2c = 2(a + b + c). If the even numbers are an arithmetic sequence, you can use the formula for the sum of an arithmetic sequence. Similarly if they are a geometric sequence.
It is the start of an arithmetic sequence.
Arithmetic