# Solve the following

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

$a_{7}=2 \times 7+7=21$