it is 8.
5
4,8,12,16,20
2
5, 11, 17, 23, 29
a1=2 d=3 an=a1+(n-1)d i.e. 2,5,8,11,14,17....
They are 14, 42, 126, 378 and 1134.
20, 15, 10, 5, 0, -5, -10, -15, -20 and so on.
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 ).
A geometric sequence with 5 terms can alternate by having positive and negative terms. For example, one such sequence could be (2, -6, 18, -54, 162). Here, the first term is (2) and the common ratio is (-3), leading to alternating signs while maintaining the geometric property.
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.
37
The sum of the terms in a sequence is called a series. Sequence is a function whose domain is the natural numbers. So f(1)= first entry in the sequence, and f(2) is the next.... f(n) is the nth term. We usually don't write sequences that way. Instead of f(1) we write, a1 to refer to the first term. The function tells us the rule we use to find the terms of the sequence. So for example, f says take n and square it. Then the first 3 terms of the sequence are 1, 4 and 9 and the first 3 terms of the series are 1, 5 and 14