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Question

 Find the sum of the first 31 terms of an AP whose n
th term is given by 3 + 2n/3


Solution

Not sure if it is 3+2n/3 or (3+2n)/3. I will work out for both cases
nth term = 3+2n/3 So first term = 3+2/3 = 11/3 and second term = 3+4/3= 13/3
so d = 2nd term - 1st term = 13/3-11/3= 2/3
Sum of 1st 31 terms is given by the formula Sn = n/2[2a+(n-1)d]
or S31 = (31/2)[2(11/3)+(31-1)(2/3)]= (31/2)[22/3 + 60/3]= (31/2)[82/3] = 1271/3  Answer

nth term = (3+2n)/3 
Here first term = (3+2)/3 = 5/3 and 2nd term = (3+4)/3 = 7/3
so d= 7/3-5/3= 2/3
S31 = 31/2[2(5/3)+(31-1)(2/3)] = 31/2[10/3+60/3]= 31/2[70/3] = 1085/3  Answer

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