Question

5 term and 21 term ap are 14 and -14 which term of an ap is zero​

Answer 1

therefore 13th term of an ap is zero
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Answer 2

Correct Question :-

If the 5th term and 21st term of an ap are 14 and -14 respectively then which term of the ap is zero.

Answer :-

If the 5th term and 21st term of an ap are 14 and -14 respectively then 13th term of the ap is zero.

Given :-

5th term and 21st term of an ap are 14 and -14.

Find :-

Which term of ap is zero.

SoLuTioN :-

Now, required formula :-

nth term = a + ( n - 1 )d, where

a is first term

d is common difference.

Consider the first term of this AP be a and common difference be d.

↠ 5th term = 14

↠ a + 4d = 14

↠ a = 14 - 4d - 1 .......(1)

↠ 21st term = - 14

↠ a + 20d = - 14

From (1) equation

↠ 14 - 4d + 20d = - 14

↠ 16d = - 14 - 14

↠ 16d = - 28

↠ d = - 28/16

↠ d = - 7/4

So,

↠ a = 14 - 4(-7/4)

↠ a = 14 + 7

↠ a = 21

Now, Consider xth term be 0 then

↠ 0 = 21 + ( x - 1 )(-7/4)

↠ - 21 = ( x - 1 )(-7/4)

↠ 21 = (x-1)(7/4)

↠ ( 21 * 4 / 7 ) = x - 1

↠ 12 = x - 1

↠ 13 = x

Therefore ,

13th term is 0.