Question

if the 11th term of an ap is zero prove that the 31st term is double the 21st term

Answer 1

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Answer 2

An arithmetic progression is a sequence of real numbers such that the difference between two consecutive terms is a constant.

nth term in A.P is is given by : a(n) = a+(n-1)d  , where n = 1, 2,3 ,4 ,5 ,....

m where a= first term

d= Common difference.

Explanation:

We are given that :  11th term of an ap is zero

i.e. a+10 d= 0

⇒ a= -10d

Consider 21st term =$a(21)= a+20d = -10d+20d=10d$

Now , Consider 31st term : $a(30) = a+30d = -10d+30d =20d$

$= 2(10d)$$= 2(a(21) )$

Hence, the 31st term is double the 21st term proved.

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6th term of ap is zero. Prove that it's 21st terms is triple its 11th term

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