Question

The n^th term of the series 2 + 4 + 7 + 11 + ..... is

विकल्प

• `1/2 (n^2 + n + 1)`

• `1/2 (n^2 + n + 2)`

• `1/2(n^2 + 2n + 2)`

• `1/2 (n^2 + 3n + 2)`

Answer 1

`1/2 (n^2 + n + 2)`

Explanation:

Let S = 2 + 4 + 7 + 11 + ... + T_n
      S = 2 + 4 + 7 + 11 ... + T_n    
      –       –    –    –           –
                                                     
      0 = 2 + 2 + 3 + 4 + ... – T_n

T_n = 1 + 1 + 2 + 3 + 4 + ...... n terms

T_n = `1 + (n(n + 1))/2 = 1/2[n^2 + n + 2]`