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  • Brainly User
2015-11-05T08:14:05+08:00

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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:
a _{n}  = a_{1} +(n-1)(d)
where:
 a _{n} = the last term ⇒  30
a _{1} = 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:
S _{n} =  \frac{n}{2} (a _{1} +a _{n} )

S _{n} =  \frac{15}{2} (2+30)

S _{n} =   \frac{15}{2} (32)

S _{n} = 15(16)

S _{n} = 240

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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2015-11-05T22:01:48+08:00
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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