With , and n = 12, the sum of an A.P. formula:  becomes:

  

 

  



 ---------- Multiplying by LCD, 3



With , and n = 28, the sum of an A.P. formula:  becomes:

  

 

  



 ---------- Multiplying by LCD, 7



 --------- eq (i)

 -------- eq (ii)

 ------- Multiplying eq (i) by 7 ------ eq (iii)

 ---- Multiplying eq (ii) by – 3 ----- eq (iv)

- 336d = 80 ---------- Adding eqs (iv) & (iii)

d, or common difference = , or 





 ------- Substituting  for d in eq (i) 





 ------ Multiplying by LCD, 7 





, or 













Sum of the 1st 40 terms, or , or 

You can do the check!! 



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