BTGmoderatorDC wrote:If sequence S has 120 terms, what is the 105th term of S?
(1) The first term of S is −8.
(2) Each term of S after the first term is 10 more than the preceding term.
Source: Official Guide
$$S\,\,:\,\,\,\left( {{a_1},{a_2}, \ldots ,{a_{120}}} \right)$$
$$? = {a_{105}}$$
$$\left( 1 \right)\,\,{a_1} = - 8\,\,\,\,\left\{ \matrix{
\,{\rm{Take}}\,\,\left( {{a_1},{a_2}, \ldots ,{a_{120}}} \right) = \left( { - 8, - 8, \ldots , - 8} \right)\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,?\, = \,\, - 8\,\, \hfill \cr
\,{\rm{Take}}\,\,\left( {{a_1},{a_2}, \ldots ,{a_{120}}} \right) = \left( { - 8,0,0,0, \ldots ,0} \right)\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,?\, = \,\,0\,\,\, \hfill \cr} \right.$$
$$\left( 2 \right)\,\,{a_n} = {a_{n - 1}} + 10\,\,\,,\,\,\,n \ge 2\,\,\,\left\{ \matrix{
\,{\rm{Take}}\,\,\left( {{a_1},{a_2}, \ldots ,{a_{120}}} \right) = \left( {0,10,20,30, \ldots ,{\rm{something}}\,\,{\rm{even}}} \right)\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,?\,\,\, = \,\,{\rm{even}}\,\, \hfill \cr
\,{\rm{Take}}\,\,\left( {{a_1},{a_2}, \ldots ,{a_{120}}} \right) = \left( {1,11,21,31, \ldots ,{\rm{something}}\,\,{\rm{odd}}} \right)\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,?\, = \,\,{\rm{odd}}\,\,\, \hfill \cr} \right.$$
$$\left( {1 + 2} \right)\,\,\,{\rm{each}}\,\,{a_n}\,\,{\rm{is}}\,\,{\rm{unique}}\,\,\, \Rightarrow \,\,\,\,{\rm{SUFF}}.$$
This solution follows the notations and rationale taught in the GMATH method.
Regards,
Fabio. 
