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Find the number of terms in the following AP:
7, 13, 19, ..., 205
Given: AP series 7, 13, 19, ..., 205.
To find: Here we have to find the number of terms in the given AP.
Solution:
First term (a) = 7
Common difference (d) = 13 $−$ 7 = 6
Last term (an) = 205
Let the last term be the nth term
We know that the nth term of the arithmetic progression is given by (a $+$ (n $−$ 1)d).
Therefore,
a $+$ (n $−$ 1)d = 205
7 $+$ (n $−$ 1)6 = 205
7 $−$ 6 $+$ 6n = 205
1 $+$ 6n = 205
6n = 205 $−$ 1
n = $\frac{204}{6}$
n = 34
So, number of terms in the given sequence is 34.
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