Question

Add 1/2+1+2+3 to 8 terms
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Answer 1

Answer:

Sum of the Terms of an Arithmetic Sequence (Arithmetic Series)

To find the sum of the first n terms of an arithmetic sequence use the formula,

S n = n ( a 1   +   a 2 ) 2 ,

where n is the number of terms, a 1 is the first term and a n is the last term.

Example 1:

Find the sum of the first 20 terms of the arithmetic series if a 1 = 5 and a 20 = 62 .

S 20 = 20 ( 5   +   62 ) 2 S 20 = 670

Example 2:

Find the sum of the first 40 terms of the arithmetic sequence

2 , 5 , 8 , 11 , 14 , ⋯

First find the 40 th term:

a 40 = a 1 + ( n − 1 ) d                 = 2 + 39 ( 3 ) = 119

Then find the sum:

S n = n ( a 1   +   a n ) 2 S 40 = 40 ( 2   +   119 ) 2 = 2420

Example 3:

Find the sum:

∑ k = 1 50 ( 3 k + 2 )

First find a 1 and a 50 :

a 1 = 3 ( 1 ) + 2 = 5 a 20 = 3 ( 50 ) + 2 = 152

Then find the sum:

S k = k ( a 1   +   a k ) 2 S 50 = 50 ( 5   +   152 ) 2 = 3925

Step-by-step explanation:

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