what is the tern associated in getting the sum of the terms of given arthmetic
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what is the tern associated in getting the sum of the terms of given arthmetic
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Step-by-step explanation: Sum of the First n Terms of an Arithmetic Sequence
Suppose a sequence of numbers is arithmetic (that is, it increases or decreases by a constant amount each term), and you want to find the sum of the first n terms.
Denote this partial sum by Sn . Then
Sn=n(a1 + an)2 ,
where n is the number of terms, a1 is the first term and an is the last term.
The sum of the first n terms of an arithmetic sequence is called an arithmetic series .
Example 1:
Find the sum of the first 20 terms of the arithmetic series if a1=5 and a20=62 .
S20=20(5 + 62)2S20=670
Example 2:
Find the sum of the first 40 terms of the arithmetic sequence 2,5,8,11,⋯ .
First find the 40th term:
a40=a1+(n−1)d =2+39(3)=119
Then find the sum:
Sn=n(a1 + an)2S40=40(2 + 119)2=2420
Example 3:
Find the sum:
∑k=150(3k+2)
First find a1 and a50 :
a1=3(1)+2=5a50=3(50)+2=152
Then find the sum:
Sk=k(a1 + ak)2S50=50(5 + 152)2=3925
See also: sigma notation of a series and nth term of an arithmetic sequence
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