Answer:
Step-by-step explanation:
This is an arithmetic sequence because each term subtracted by the previous term is a constant called the common difference.
an=a+d(n-1) where a is the initial term and d is the common difference
a=-20 and d=-16+20=4 so
an=-20+4(n-1)
an=4n-24
The sum of an arithmetic sequence is the average of the first and last terms times the number of terms
sn=(a1+an)(n/2)
s30=(-20+4(30)-24)(30/2)
s30=1140
The sum of the first 30 terms of the sequence –20, –16, –12, –8, –4, . . . is obtained being 1140
Arithmetic sequence is a sequence where each consequtive term has a common constant difference.
An arithmetic sequence, therefore, is defined by two parameters, viz. the starting term and the common difference.
Let the starting term be 'a' and common difference be 'd', then we get the arithmetic sequence as:
[tex]\rm a, a+d, a+2d, \cdots[/tex]
The sum of the first 'n' terms of that sequence is is:
[tex]\rm a + (a+d) + (a+2d) + \cdots + (a+(n-1)d) = \dfrac{n}{2}[2a + (n-1)d ][/tex]
For this case, the series –20, –16, –12, –8, –4, . . . starts from a = -20,
and each next term is obtained by adding d = 4 in previous term.
Thus, the sum of the first n = 30 terms of that sequence is evaluated as:
[tex]S_n = \dfrac{n}{2}[2a + (n-1)d ]\\\\S_{30} = \dfrac{30}{2}[2(-20) + (30-1)(4) ] = 15(-40 +116) = 15 \times 76 = 1140[/tex]
Thus, the sum of the first 30 terms of the sequence –20, –16, –12, –8, –4, . . . is obtained being 1140
Learn more about arithmetic sequence here:
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