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In an A.P. (arithmetic progression), the first term is 1 and the common difference is 4. How many terms of the A.P must be taken for their sum to be equal to 120?

 Jan 24, 2021
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Let  the last term be    1 + 4(n  -1)     where  n is the  total number  of terms

 

Sum of an arithmetic series = 

 

(first term + last term )  (number of terms   /2)

 

So we have

 

( 1   +1 + 4(n - 1) )  (n/2)   = 120           simplify

 

( 4n  -2)  (n/2)  =120   

 

(2 n -1)  n   =120

 

2n^2  - n  =120

 

2n^2  - n    -120    =  0   

 

(2n  + 15)  ( n  - 8)    = 0

 

The second factor  set  to   0  and solved for n gives us  our  answer  = 8 terms

 

 

cool cool cool

 Jan 24, 2021

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