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Question
The nth term of a sequence is given by an = 2n + 7. Show that it is an A.P. Also, find its 7th term.
Solution
\[a_n = 2n + 7\]
\[ \therefore a_1 = 2 \times 1 + 7 = 9\]
\[ a_2 = 2 \times 2 + 7 = 11\]
\[ a_3 = 2 \times 3 + 7 = 13\]
\[ a_4 = 2 \times 4 + 7 = 15\]
\[\text { and so on }\]
\[\text { So, common difference }\left( d \right) = 11 - 9 = 2\]
\[\text { Thus, the above sequence is an A . P . with the common difference as} 2\]
\[ a_7 = 2 \times 7 + 7 = 21\]
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