Question

# The number of terms in an $$A.P.$$ is even; the sum of the odd terms in it is $$24$$ and that the even terms is $$30$$. If the last term exceeds the first term by $$10\dfrac {1}{2}$$, then the number of terms in the $$A.P.$$ is :

A
4
B
8
C
12
D
16

Solution

## The correct option is B $$8$$Let $$'a'$$ and $$'d'$$ be the first term and common difference of the series respectively.Let $$'2n'$$ be the total terms present in the series.Now, from the given condition we get$$\displaystyle \frac{n}{2}[2a+(n-1)2d]=24$$ - (for odd terms).............(1)$$\displaystyle \frac{n}{2}[2a+2d +(n-1)2d]=30$$ - (for even terms)...........(2)Subtract (1) from (2),$$nd=6$$.......................(3)$$a+(2n-1)d-a=10.5$$.............(4)$$2nd-d=10.5$$$$d=12-10.5$$.........(from 3)$$d=1.5$$$$\displaystyle n= \frac{6}{1.5}=4$$Total number of terms are $$'2n'$$ i.e. $$8$$Mathematics

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