find the sum of first 11 terms of 8,15,22,29 sequence

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lemjay's profile pic

lemjay | High School Teacher | (Level 3) Senior Educator

Posted on

First, determine if the given is an arithmetic sequence. To do so, get the difference between
consecutive terms.

`d=22-8=7`

`d=22-15=7`

`d=29-22=7`

Since the difference between consecutive terms are the same, then 8 , 15, 22,29 is an arithmetic sequence.

So, to get the sum of the first 11 terms, the 11th term must be determine. To do so, apply the formula:

`a_n=a_1+(n-1)d`

Plug-in n=11, a1=8 and d=7.

`a_11=8+(11-1)7`

`a_11=8+10*7`

`a_11=78`

Now that the 11th term is known, use the formula:

`S_n=(n(a_1+a_n))/2`

Plug-in n=11, a1=8 and a11=78 .

`S_11=(11*(8+78))/2`

`S_11=(11*86)/2`

`S_11=473`

Hence, the sum of the first 11 terms of the given sequence is 473.

amysor's profile pic

amysor | Student, Grade 10 | (Level 1) Valedictorian

Posted on

The pattern is +7. So the first 11 terms are 8, 15, 22, 29, 36, 43, 50, 57, 64, 71, 78. The sum of all these numbers would be 473.

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