Q : 5     Find the number of terms in each of the following APs :

            (i)  \small 7,13,19,...,205

Answers (1)

Given AP series is 
\small 7,13,19,...,205
Let's suppose there are n terms in given AP
Then, 
a = 7 , a_n = 205
And 
d= a_2-a_1 = 13-7 = 6
Now, we know that
a_n =a + (n-1)d
\Rightarrow 205=7 + (n-1)6
\Rightarrow 205-7 = 6n-6
\Rightarrow n = \frac{198+6}{6} = \frac{204}{6} = 34
Therefore, there are 34 terms in given AP
 

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