Find sum of series 1-3+5-7+9-11+......Upto n terms when
Answers
the first sequence and n terms of the second sequence:
1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 + 21 + 23 + ... + 3nth term
-10 - 22 - 34 - 46 - ... - nth term
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1 + 3 - 5 + 7 + 9 - 11 + 13 + 15 - 17 + 19 + 21 - 23 + ... ?
The first sequence has 3n terms, but first we find the sum of n terms
S%5Bn%5DAMP Parsing Error of '''=''': Invalid expression '''=''': syntax error at /home/ichudov/project_locations/algebra.com/templates/Algebra/Expression.pm line 194.
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AMP Parsing Error of 'expr(n/2)*(2a[1]^''+(n-1)d^'')': Invalid expression '''+(n-1)d^'')': syntax error at /home/ichudov/project_locations/algebra.com/templates/Algebra/Expression.pm line 194.
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AMP Parsing Error of '''=''': Invalid expression '''=''': syntax error at /home/ichudov/project_locations/algebra.com/templates/Algebra/Expression.pm line 194.
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AMP Parsing Error of 'expr(n/2)*(2(1)^''+(n-1)2^'')': Invalid expression '''+(n-1)2^'')': syntax error at /home/ichudov/project_locations/algebra.com/templates/Algebra/Expression.pm line 194.
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AMP Parsing Error of '''=''': Invalid expression '''=''': syntax error at /home/ichudov/project_locations/algebra.com/templates/Algebra/Expression.pm line 194.
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expr%28n%2F2%29%2A%282%2B2n-2%29AMP Parsing Error of '''=''': Invalid expression '''=''': syntax error at /home/ichudov/project_locations/algebra.com/templates/Algebra/Expression.pm line 194.
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expr%28n%2F2%29%2A%282n%29AMP Parsing Error of '''=''': Invalid expression '''=''': syntax error at /home/ichudov/project_locations/algebra.com/templates/Algebra/Expression.pm line 194.
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n%5E2
and since it has 3n terms, we replace n by 3n and get the sum of 3n terms,
%283n%29%5E2 or 9n%5E2
The second sequence -10-22-34-46- ... has only n terms:
S%5Bn%5DAMP Parsing Error of '''=''': Invalid expression '''=''': syntax error at /home/ichudov/project_locations/algebra.com/templates/Algebra/Expression.pm line 194.
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AMP Parsing Error of 'expr(n/2)*(2a[1]^''+(n-1)d^'')': Invalid expression '''+(n-1)d^'')': syntax error at /home/ichudov/project_locations/algebra.com/templates/Algebra/Expression.pm line 194.
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AMP Parsing Error of '''=''': Invalid expression '''=''': syntax error at /home/ichudov/project_locations/algebra.com/templates/Algebra/Expression.pm line 194.
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AMP Parsing Error of 'expr(n/2)*(2(-10)^''+(n-1)(-12)^'')': Invalid expression '''+(n-1)(-12)^'')': syntax error at /home/ichudov/project_locations/algebra.com/templates/Algebra/Expression.pm line 194.
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AMP Parsing Error of '''=''': Invalid expression '''=''': syntax error at /home/ichudov/project_locations/algebra.com/templates/Algebra/Expression.pm line 194.
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expr%28n%2F2%29%2A%28-20-12n%2B12%29AMP Parsing Error of '''=''': Invalid expression '''=''': syntax error at /home/ichudov/project_locations/algebra.com/templates/Algebra/Expression.pm line 194.
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expr%28n%2F2%29%2A%28-8-12n%29AMP Parsing Error of '''=''': Invalid expression '''=''': syntax error at /home/ichudov/project_locations/algebra.com/templates/Algebra/Expression.pm line 194.
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expr%28n%2F2%29%2A2%28-4-6n%29AMP Parsing Error of '''=''': Invalid expression '''=''': syntax error at /home/ichudov/project_locations/algebra.com/templates/Algebra/Expression.pm line 194.
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n%2A%28-4-6n%29AMP Parsing Error of '''=''': Invalid expression '''=''': syntax error at /home/ichudov/project_locations/algebra.com/templates/Algebra/Expression.pm line 194.
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-4n-6n%5E2
Adding the two sums: 9n%5E2-4n-6n%5E2AMP Parsing Error of '''=''': Invalid expression '''=''': syntax error at /home/ichudov/project_locations/algebra.com/templates/Algebra/Expression.pm line 194.
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3n%5E2-4n
Answer: 3n%5E2-4n