Learning Task 4: Find the pattern and write its expression,
1. 12, 15, 18,21,24,...
NEED KO NA PO NOW
KUNG SINO MAKASAGOT MAY 50 POINTS UNG TAMA PO SANA SAGOT NYO
Share
Learning Task 4: Find the pattern and write its expression,
1. 12, 15, 18,21,24,...
NEED KO NA PO NOW
KUNG SINO MAKASAGOT MAY 50 POINTS UNG TAMA PO SANA SAGOT NYO
Sign Up to our social questions and Answers Engine to ask questions, answer people’s questions, and connect with other people.
Login to our social questions & Answers Engine to ask questions answer people’s questions & connect with other people.
Verified answer
Answer:
12,15,18,21,24
Your input 12,15,18,21,24 appears to be an arithmetic sequence
Find the difference between the members
a2-a1=15-12=3
a3-a2=18-15=3
a4-a3=21-18=3
a5-a4=24-21=3
The difference between every two adjacent members of the series is constant and equal to 3
General Form: a
n
=a
1
+(n-1)d
a
n
=12+(n-1)3
a1=12 (this is the 1st member)
an=24 (this is the last/nth member)
d=3 (this is the difference between consecutive members)
n=5 (this is the number of members)
Sum of finite series members
The sum of the members of a finite arithmetic progression is called an arithmetic series.
Using our example, consider the sum:
12+15+18+21+24
This sum can be found quickly by taking the number n of terms being added (here 5), multiplying by the sum of the first and last number in the progression (here 12 + 24 = 36), and dividing by 2:
n(a1+an)
2
5(12+24)
2
The sum of the 5 members of this series is 90
This series corresponds to the following straight line y=3x+12
Finding the n
th
element
a1 =a1+(n-1)*d =12+(1-1)*3 =12
a2 =a1+(n-1)*d =12+(2-1)*3 =15
a3 =a1+(n-1)*d =12+(3-1)*3 =18
a4 =a1+(n-1)*d =12+(4-1)*3 =21
a5 =a1+(n-1)*d =12+(5-1)*3 =24
a6 =a1+(n-1)*d =12+(6-1)*3 =27
a7 =a1+(n-1)*d =12+(7-1)*3 =30
a8 =a1+(n-1)*d =12+(8-1)*3 =33
a9 =a1+(n-1)*d =12+(9-1)*3 =36
a10 =a1+(n-1)*d =12+(10-1)*3 =39
a11 =a1+(n-1)*d =12+(11-1)*3 =42
a12 =a1+(n-1)*d =12+(12-1)*3 =45
a13 =a1+(n-1)*d =12+(13-1)*3 =48
a14 =a1+(n-1)*d =12+(14-1)*3 =51
a15 =a1+(n-1)*d =12+(15-1)*3 =54
a16 =a1+(n-1)*d =12+(16-1)*3 =57
a17 =a1+(n-1)*d =12+(17-1)*3 =60
a18 =a1+(n-1)*d =12+(18-1)*3 =63
a19 =a1+(n-1)*d =12+(19-1)*3 =66
a20 =a1+(n-1)*d =12+(20-1)*3 =69
a21 =a1+(n-1)*d =12+(21-1)*3 =72
a22 =a1+(n-1)*d =12+(22-1)*3 =75
a23 =a1+(n-1)*d =12+(23-1)*3 =78
a24 =a1+(n-1)*d =12+(24-1)*3 =81
a25 =a1+(n-1)*d =12+(25-1)*3 =84
a26 =a1+(n-1)*d =12+(26-1)*3 =87
a27 =a1+(n-1)*d =12+(27-1)*3 =90
a28 =a1+(n-1)*d =12+(28-1)*3 =93
a29 =a1+(n-1)*d =12+(29-1)*3 =96
a30 =a1+(n-1)*d =12+(30-1)*3 =99
Pattern : n+3
..27, 30, 33 and so on