Question

# If $$7$$ times the $$7^{th}$$ term of an AP is equal to $$11$$ times its $$11^{th}$$ term, then its $$18^{th}$$ term will be

A
7
B
11
C
18
D
0

Solution

## The correct option is C $$0$$Let first term and common difference be $$a,d$$ respectively.nth term $$t_{n}= a+(n-1)d$$$$7^{th}$$ term= $$a + 6d$$$$11^{th}$$ term= $$a + 10d$$Given,$$7$$ times $$7^{th}$$ term=$$11$$ times $$11^{th}$$ term$$7\times (a+6d)$$=$$11\times(a+10d)$$$$\Rightarrow 7a + 42d = 11a + 110d$$$$\Rightarrow 4a + 68d=0$$$$\Rightarrow a + 17d= 0$$  Comparing with $$t_{n}= a+(n-1)d$$, we get $$n=18$$.The $$18^{th}$$ term is $$0$$.Mathematics

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