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High School Math Problems/Sequences using sigma

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Need help solving problem numbers 6,8,9,10,11, 12,13,14,15,16 and show work.

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6.What is the tenth term of the geometric progression ½, -1, 2, -4?
8.Which series is represented by ∑_(i=1)^4▒〖(4i-2)〗
9.What type of series is 32+16+8+4+2+1?
10.What is a rule for the nth term of the geometric sequence with a3= -12 and common ratio r=3
11.What is the sum of the series∑_(i=0)^9▒〖20〖(1/2)〗^i 〗
12.What is the sum of the series ∑_(i=0)^5▒〖(n^3+3)〗
13..What is the rule for the nth term of the arithmetic sequence with a14=9 and common difference d=2
14.What is the sum of the first 50 terms of the series 2+17+32+47+......?

15.Choose the statement that is true about the given quantities.
Column A. Tenth term of the sequence : an=2n-5 Column B: ∑_(n=1)^5▒n

Column A:The common ratio of the geometric sequence - 1/9+ 1/3-1+3 : Column B: ∑_(n=3)^6▒〖(-2)〗^n
A. The quantity in column A is greater
B. The quantity in column B is greater
C.The two quantities are equal
D. The relationship cannot be determined from the given information.

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Sandhya Sharma, MSc
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  • MSc, Meerut University
  • MPhil, Institute of Advanced Studies
  • MSc, AIT
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