Question

Find the 10th term of the AP whose sum of n term is given by 2(n)(n)+3n

Answer 1

We have,

Sn = 2n² + 3n

∴S1 = 2(1)²+3(1)
        = 2+3
       = 5
       = a        ( first term)

S2 = 2(2)² +3(2)
      =8+6
      = 14

Now,
a + a2 = S2
⇒ 5 + a2 = 14
⇒ a2 = 9

Also,
a2-a1 = d
⇒ d = 9-5 
       = 4

we have, a=5 and d=4

∴a10 = a+9d
         = 5+9(4)
         = 41