Show that

    \[{{\mathbf{a}}_{\mathbf{1}}},\text{ }{{\mathbf{a}}_{\mathbf{2}}},\text{ }{{\mathbf{a}}_{\mathbf{3}}},\text{ }\ldots \]

form an A.P. where an is defined as

    \[{{\mathbf{a}}_{\mathbf{n}}}~=\text{ }\mathbf{3}\text{ }+\text{ }\mathbf{4n}\]

. Also find the sum of first

    \[15\]

terms.