Write this series  in sigma notation and find its sum 1+8+15+....+43Please explain process

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embizze's profile pic

embizze | High School Teacher | (Level 1) Educator Emeritus

Posted on

Write the finite series 1+8+15+...+43 in sigma notation:

Note that this is an arithmetic series; the underlying arithmetic sequence has first term `a_1=1` and common difference `d=7` .

The formula for the `nth` term of an arithmetic sequence is `a_n=a_1+(n-1)d` (You start with the first term; the second term you add 1 d, the third term you add another d which is the first term plus 2 d's, etc...)

Thus we can find which term 43 is: 43=1+(n-1)7

43=1+7n-7

7n=49

n=7 So 43 is the 7th term in the sequence; the series has 7 terms.

The nth term of the sequence is 1+(n-1)7 or 7n-6

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The sum can be represented as `sum_(i=1)^7 7n-6`

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**When i=1 you have 7(1)-6=1

When i=2 you have 1 (the pervious term) + 7(2)-6 or 1+8

i=3 ==> 1+8+7(3)-6 or 1+8+15

etc...

Sources:
salonigaba's profile pic

salonigaba | Student, Grade 11 | (Level 1) Salutatorian

Posted on

an= a1+(n-1)d

a1=1,d=7,an=43.

so n=7,

sum will be:sumation(limit of i will be 1 to 7){7n-6}

1+8+15.

 

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