The $n^{t h}$ term of a sequence is given by $a_{n} = 2 n + 7$ . Show that it is an A.P. Also, find its $7^{t h}$ term.

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Solution

$a_{n} = 2 n + 7$

$a_{1} = 2 (1) + 7 = 9$

$a_{2} = 2 (2) + 7 = 11$

$a_{3} = 2 (3) + 7 = 13$

Hence the common difference (d),

$a_{3} - a_{2} = a_{2} - a_{1} = 2$

$∴$ The given sequence is A.P.

$a_{7} = 2 (7) + 7 = 21$

7th term is 21.

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