Question

The sum of the 2nd and 19th arithmetric progression is equal to the 8th,12th and 15th elements of the progression. then which element should be equal to zero​

Answer 1

Answer:

13th element would be equal to zero

Step-by-step explanation:

let say ap is

a , a+d , a + 2d

2nd = a+2d

19th = a + 18d

sum = 2a + 20d

8th = a + 7d

12th = a+ 11d

15th = a + 14d

sum = 3a +32d

equating both

2a+ 20d = 3a + 32d

a + 12d = 0

a + (13-1)d = 0

13th element would be equal to zero

Answer 2

ANSWER

Let the first term of AP be a and difference be d

Then third term will be =a+2d

${15}^{th} \: will \: be = a + 14d$

${6}^{th} \: will \: be = a + 5d$

$1 {1}^{th} \: will \: be = a + 10d$

$1 {3}^{th} will \: be = a + 12d$

$then \: the \: eq. \: will \: be$

$a + 2d + a + 14d = a + 5d + a + 10d + a + 12d$

$= > 2a + 16d = 3a + 27d$

$= > a + 11d = 0$

$we \: understand \: a + 11d \: will \: be \: the \: 1 {2}^{th} \: term \: of \: arithmetic \: progression.$

$so, \: CORRECT \: answer \: is \: {\boxed {\pink{12}}}$

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