Question 1032522
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11. Find the sum of the arithmetic sequence  2, 4, 6, 8, ..., 70.


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On arithmetic progressions, read the lesson <A HREF=https://www.algebra.com/algebra/homework/Sequences-and-series/Arithmetic-progressions.lesson>Arithmetic progressions</A> in this site.

The given progression is AP with the first term 2 and the common difference 2.
It contains all even integers between 2 and 70, inclusively.
The number of the terms is {{{70/2}}} = 35.

Use the formula for the sum of an AP

S = {{{((a[1]+a[n])*n)/2}}} = {{{((2+70)*35)/2}}}.

Calculate it yourself.
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12. Find the sum of the geometric sequence  42, 7, 7/6,. . . , 42*(1/6)^8


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The last term of the progression was written INCORRECTLY. I fixed it.


On geometric progressions, read the lesson <A HREF=https://www.algebra.com/algebra/homework/Sequences-and-series/Geometric-progressions.lesson>Geometric progressions</A> in this site.

The given progression is GP with the first term 42 and the common ratio {{{1/6}}}.
The number of the terms is 9.

Use the formula for the sum of a GP

S = {{{a[1]*((q^n-1)/(q-1))}}} = {{{42*(((1/6)^n-1)/((1/6)-1)))}}} = {{{42*(((1-6^n)*6)/(6^n*(1-6)))}}} = {{{42*(((6^n-1)*6)/((6-1)*6^n)))}}} = {{{((42*6)/5)*((6^n-1)/6^n)}}} = {{{((42*6)/5)*((6^9-1)/6^9)}}}.

Calculate it yourself.
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