The sum of the terms of each finite sequence
1. 22
2. 35
3. -15
4. 231
5. -57
Further explanation
Arithmetic sequence is an arrangement of numbers that has the same difference for consecutive pairs of numbers or it can be said that "the difference between one term and the next is a constant. (adding the same number to the next number)
"
The arrangement of the numbers is like this:
[tex]\rm a,a+d,a+2d,a+3d,a+4d..etc[/tex]
a = initial term
d = different (common difference)
The formula for the nth term:
[tex]\rm \boxed{\bold{xn=a+d(n-1)}}[/tex]
While the formula for the sum of n terms:
[tex]\rm \boxed{\bold{\dfrac{1}{2}n(2a+(n-1)d}}[/tex]
From the problems above, it can be said that the series is an arithmetic sequence because they have the same difference
a = 1
d = 3
n = 4
[tex]\rm =\dfrac{1}{2}.4(2.1+(4-1)3)\\\\=2(2+9)\\\\=\boxed{\bold{22}}[/tex]
a = 3
d = 2
n = 5
[tex]\rm =\dfrac{1}{2}.5(2.3+(5-1)2)\\\\=\boxed{\bold{35}}[/tex]
a = 10
d = -5
n = 6
[tex]\rm =\dfrac{1}{2}.6(2.10+(6-1).-5)\\\\=3(20-25)\\\\=\boxed{\bold{-15}}[/tex]
a = 81
d = -17
n = 6
[tex]\rm =\dfrac{1}{2}.6(2.81+(6-1).-17)\\\\=3(162-85)\\\\=\boxed{\bold{231}}[/tex]
-
-2, -5, -8, -11, -14, -17
a = -2
d = -3
n = 6
[tex]\rm =\dfrac{1}{2}.6(2.-2+(6-1).-3)\\\\=3(-4-15)\\\\=\boxed{\bold{-57}}[/tex]
Learn more
commoon difference of the sequence
https://brainly.ph/question/1721583
Insert two aritmetic means
https://brainly.ph/question/1543769
https://brainly.ph/question/1838784
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