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:
$a_{n}=2 n+7$
$\therefore a_{1}=2 \times 1+7=9$
$a_{2}=2 \times 2+7=11$
$a_{3}=2 \times 3+7=13$
$a_{4}=2 \times 4+7=15$
and so on
So, common difference $(d)=11-9=2$
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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