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  • Find the number of terms in each of the following APs : (i) 18, 15 1/2, 13, ..., -47

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

             (ii)   \small 18,15\frac{1}{2},13,...,-47

Answers (1)

best_answer

Given AP series is 
\small 18,15\frac{1}{2},13,...,-47
suppose there are n terms in given AP
Then, 
a = 18 , a_n = -47
And 
d= a_2-a_1 = \frac{31}{2}-18 = \frac{31-36}{2} = -\frac{5}{2}
Now, we know that
a_n =a + (n-1)d
\Rightarrow -47=18 + (n-1)\left ( -\frac{5}{2} \right )
\Rightarrow -47-18= -\frac{5n}{2}+\frac{5}{2}
\Rightarrow -\frac{5n}{2}= -65-\frac{5}{2}
\Rightarrow -\frac{5n}{2}= -\frac{135}{2}
\Rightarrow n = 27
Therefore, there are 27 terms in given AP

Posted by

Gautam harsolia

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