Question

4. If for a sequence (an), S, = 2n^2 + 9n, where, S is the sum of n terms, the value of a20 ( Term 20 ) is
(b) 75
(c) 87
(d) 97
(a) 65​

Answer 1

Answer:

an = Sn - Sn-1  

    = (2n^2 +9n) -  [2(n-1)^2 + 9(n-1)]

    = (2n^2 + 9n) - [2(n^2 + 1 - 2n) + 9n - 9 ]

    = (2n^2 + 9n) - (2n^2 +2 - 4n +9n -9)

    = 2n^2 + 9n - 2n^2 - 2 +4n - 9n + 9

therefore,      an = 4n + 2

so a20 = 4(20) + 7

            = 80 +7

            =  87

hence option (c) is correct.