SOLUTION: Partial Sum of a Geometric Sequence Find the sum of the first ten terms of the sequence a + b, a^2 + 2b, a^3 + 3b, a^4 + 4b,...

Question 1199272: Partial Sum of a Geometric Sequence Find the sum of the first ten terms of the sequence
a + b, a^2 + 2b, a^3 + 3b, a^4 + 4b,...
Answer by ikleyn(52787) (Show Source): You can put this solution on YOUR website!
.
Partial Sum of a Geometric Sequence Find the sum of the first ten terms of the sequence
a + b, a^2 + 2b, a^3 + 3b, a^4 + 4b,...
~~~~~~~~~~~~~~~~~

Split your partial sum into the sum of two sequances.


One sequence is a geometric progression

    a,  a^2,  a^3,  a^4,  . . . ,  a^10.    (1)


The other sequence is an arithmetic progression

    b,  2b,  3b,  4b,  . . . ,  10b.        (2)


Then apply standard formulas to each sequence separately.


As the last step, combine two formulas together.


ANSWER.  The sum is  S =  + 55b.

Solved.

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For introductory lessons on arithmetic and geometric progressions see
    - Arithmetic progressions
    - The proofs of the formulas for arithmetic progressions
    - Problems on arithmetic progressions
    - Word problems on arithmetic progressions

    - Geometric progressions
    - The proofs of the formulas for geometric progressions
    - Problems on geometric progressions
    - Word problems on geometric progressions
in this site.

Also, you have this free of charge online textbook in ALGEBRA-II in this site
    - ALGEBRA-II - YOUR ONLINE TEXTBOOK.

The referred lessons are the part of this online textbook under the topics
"Arithmetic progressions" and "Geometric progressions".

Save the link to this textbook together with its description

Free of charge online textbook in ALGEBRA-II
https://www.algebra.com/algebra/homework/complex/ALGEBRA-II-YOUR-ONLINE-TEXTBOOK.lesson

into your archive and use when it is needed.

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