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?
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an = a1 + d(n - 1)
It is an arithmetic sequence for which the index goes on and on (and on).
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.
Arithmetic