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Sagot :
Sum of even numbers not more than 30. (Not more 30 means 30 is included. Use the symbol ≤)
= {x/x is an even number ≤ 30 }
= {2, 4, ... 30]
The difference (d) between any two consecutive numbers = 2
Steps:
1) Find the number of terms in a sequence of even numbers up to 30. The pattern/rule is:
[tex]a _{n} = a_{1} +(n-1)(d)[/tex]
where:
[tex]a _{n} [/tex] = the last term ⇒ 30
[tex]a _{1} [/tex] = is the first term ⇒ 2
d (difference) = 2
2) Solve for n:
30 = 2 + (n - 1) (2)
30 = 2 + 2n - 2
30 = 2n
2n/2 = 30/2
n = 15
The number of terms in the given sequence is 15.
3) Solve for the sum of the sequence:
[tex]S _{n} = \frac{n}{2} (a _{1} +a _{n} )[/tex]
[tex]S _{n} = \frac{15}{2} (2+30)[/tex]
[tex]S _{n} = \frac{15}{2} (32)[/tex]
[tex]S _{n} = 15(16)[/tex]
[tex]S _{n} = 240[/tex]
The sum of even numbers not more than 30 is 240.
(Note: I assume that you are reviewing for MTAP, because this is an advance topic for Grade 2 or 3 student.}
= {x/x is an even number ≤ 30 }
= {2, 4, ... 30]
The difference (d) between any two consecutive numbers = 2
Steps:
1) Find the number of terms in a sequence of even numbers up to 30. The pattern/rule is:
[tex]a _{n} = a_{1} +(n-1)(d)[/tex]
where:
[tex]a _{n} [/tex] = the last term ⇒ 30
[tex]a _{1} [/tex] = is the first term ⇒ 2
d (difference) = 2
2) Solve for n:
30 = 2 + (n - 1) (2)
30 = 2 + 2n - 2
30 = 2n
2n/2 = 30/2
n = 15
The number of terms in the given sequence is 15.
3) Solve for the sum of the sequence:
[tex]S _{n} = \frac{n}{2} (a _{1} +a _{n} )[/tex]
[tex]S _{n} = \frac{15}{2} (2+30)[/tex]
[tex]S _{n} = \frac{15}{2} (32)[/tex]
[tex]S _{n} = 15(16)[/tex]
[tex]S _{n} = 240[/tex]
The sum of even numbers not more than 30 is 240.
(Note: I assume that you are reviewing for MTAP, because this is an advance topic for Grade 2 or 3 student.}
Sum of even numbers not more than 30. (Not more 30 means 30 is included. Use the symbol ≤)
= {x/x is an even number ≤ 30 }
= {2, 4, ... 30]
The difference (d) between any two consecutive numbers = 2
Steps:
1) Find the number of terms in a sequence of even numbers up to 30. The pattern/rule is:
where:
= the last term ⇒ 30
= is the first term ⇒ 2
d (difference) = 2
2) Solve for n:
30 = 2 + (n - 1) (2)
30 = 2 + 2n - 2
30 = 2n
2n/2 = 30/2
n = 15
The number of terms in the given sequence is 15.
3) Solve for the sum of the sequence:
The sum of even numbers not more than 30 is 240.
(Note: I assume that you are reviewing for MTAP, because this is an advance topic for Grade 2 or 3 student.}
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