the number of terms of the series 5+13+ ... that must be added so that the sum will be 495
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Given :
- First term = 5
To find :
No. of terms of the AP.
Solution :
Common difference of the AP :-
We know the formula for common difference of the AP i.e,
Where :
- d = Common Difference
- a = Any term of the AP.
Here ,
⠀⠀⠀⠀⠀⠀⠀⠀⠀a(n -1) = 1st term
⠀⠀⠀⠀⠀⠀⠀⠀⠀an = 2nd term
Now using the formula for common difference and substituting the values in it, we get :
Hence the common difference of the AP is 8.
No. of terms of the AP :
We know the formula for sum of n terms of the AP i.e,
Where :
- s = Sum of terms of the AP.
- n = No. of terms
- d = Common Difference
- a = First term
Now using the formula for sum of n terms and substituting the values in it, we get :
Since the no. of terms cannot be negative and in fraction , the actual number of terms of the AP is 11. (n = 11)
Hence their are 11 terms in the AP.
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