Find the sum of the first 12 terms of the series 5, 9, 13, 17,
Answers
Answer: Step by Step Solution
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5,9,13,17,21
Your input 5,9,13,17,21 appears to be an arithmetic sequence
Find the difference between the members
a2-a1=9-5=4
a3-a2=13-9=4
a4-a3=17-13=4
a5-a4=21-17=4
The difference between every two adjacent members of the series is constant and equal to 4
General Form: a
n
=a
1
+(n-1)d
a
n
=5+(n-1)4
a1=5 (this is the 1st member)
an=21 (this is the last/nth member)
d=4 (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:
5+9+13+17+21
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 5 + 21 = 26), and dividing by 2:
n(a1+an)
2
5(5+21)
2
The sum of the 5 members of this series is 65
This series corresponds to the following straight line y=4x+5
Finding the n
th
element
a1 =a1+(n-1)*d =5+(1-1)*4 =5
a2 =a1+(n-1)*d =5+(2-1)*4 =9
a3 =a1+(n-1)*d =5+(3-1)*4 =13
a4 =a1+(n-1)*d =5+(4-1)*4 =17
a5 =a1+(n-1)*d =5+(5-1)*4 =21
a6 =a1+(n-1)*d =5+(6-1)*4 =25
a7 =a1+(n-1)*d =5+(7-1)*4 =29
a8 =a1+(n-1)*d =5+(8-1)*4 =33
a9 =a1+(n-1)*d =5+(9-1)*4 =37
a10 =a1+(n-1)*d =5+(10-1)*4 =41
a11 =a1+(n-1)*d =5+(11-1)*4 =45
a12 =a1+(n-1)*d =5+(12-1)*4 =49
a13 =a1+(n-1)*d =5+(13-1)*4 =53
a14 =a1+(n-1)*d =5+(14-1)*4 =57
a15 =a1+(n-1)*d =5+(15-1)*4 =61
a16 =a1+(n-1)*d =5+(16-1)*4 =65
a17 =a1+(n-1)*d =5+(17-1)*4 =69
a18 =a1+(n-1)*d =5+(18-1)*4 =73
a19 =a1+(n-1)*d =5+(19-1)*4 =77
a20 =a1+(n-1)*d =5+(20-1)*4 =81
a21 =a1+(n-1)*d =5+(21-1)*4 =85
a22 =a1+(n-1)*d =5+(22-1)*4 =89
a23 =a1+(n-1)*d =5+(23-1)*4 =93
a24 =a1+(n-1)*d =5+(24-1)*4 =97
a25 =a1+(n-1)*d =5+(25-1)*4 =101
a26 =a1+(n-1)*d =5+(26-1)*4 =105
a27 =a1+(n-1)*d =5+(27-1)*4 =109
a28 =a1+(n-1)*d =5+(28-1)*4 =113
a29 =a1+(n-1)*d =5+(29-1)*4 =117
a30 =a1+(n-1)*d =5+(30-1)*4 =121
Explanation: Mark me as brainliest pls i found this answer about 1 hrs pls