Explanation

(a)
Let $S = 2 + 7 + 14 + 23 + 34 + ... + T_{n}$ …(i)
and $S = 2 + 7 + 14 + 23 + 34 + ...T_{n - 1} + T_{n}\ \ ...$(ii)
On subtracting Eqs. (i) from (ii),we get
$\therefore S - S = 2 + \left\lbrack 5 + 7 + 9 + 11 + ... + T_{n} - T_{n - 1} \right\rbrack - T_{n}$
$\Rightarrow T_{n} = 2 + \left\lbrack \frac{n - 1}{2}\{ 2 \times 5 + (n - 2)2\} \right\rbrack$
$\Rightarrow T_{n} = 2 + (n - 1)(n + 3)$
$\therefore T_{99} = 2 + 98 \times 102 = 9998$