Mathur S.

asked • 11/30/17

Find the sum of ap 7+10.5+14+...+84

Find the sum of ap
 

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Inactive Tutor answered • 11/30/17

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Common difference is 3.5
7 + 3.5 = 10.5
10.5 + 3.5 = 14
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84
 
7 + 3.5x = 84
3.5x = 77
x = 22
 
Total terms in the series is n = x+1 so n=23 terms
  
Sum = (n/2)(a1+an) = (23/2)(7+84) = (23/2)(91) = 1046.5
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Inactive Tutor

To find n the general formula is
a1 + (n-1)d = an
 
7 + (n-1)(3.5) = 84
7 + 3.5n - 3.5 = 84
3.5n + 3.5 = 84
3.5n = 80.5
n = 23 terms in sequence.  :-)
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11/30/17

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