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Show that the progression 21,16,11,6,1,…...

Show that the progression 21,16,11,6,1,…, is an AP. Write its first term and the common difference. Which term of this AP is -54?

Text Solution

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The given progression is 21,16,11,6,1…,
We have
( 16-21) = (11-16) = ( 6-110 = ( 1-6) = -5 , which is constant .
So, the given progression is an AP.
Its first term a=21 and common difference , d=-5
Let its nth term be -54. then.
` T_(n) = -54 Rightarrow a + ( n-1)d = -54`
` Rightarrow 2e1 + ( n-1) xx (-5) = -54`
` Rightarrow -54 + 26 = -54 5n = 80 Rightarrow n = 16`
` T_(16) = -54`
Hence, the 16th term of the given AP is -54
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