the sum of n terms of an AP is (2n+3n2).determine the AP and find the rth term?
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Given that
Sum of n terms = Sn = 2n + 3n²
S1 = 2(1) + 3(1)² = 5
Sum of 1st term is same as first term so a1 = a = 5
S2 = 2(2) + 3(2)² = 4 + 12 = 16
S2 = a1 + a2
16 = 5 + a2
⇒ a2 = 11
Common difference d = a2 - a1 = 11 - 5 = 6
A.P is 5 , 11 , 17 , 23 , 29 .......
rth term ar = ( 5 + ( r-1)6)
⇒ 5 + 6r - 6
⇒ 6r - 1 is rth term of A.P
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