Question

The sum of the 6th and 15th elements of an arithmetic progression is equal to the sum of 7th, 10th and 12th elements of the same progression. Which element of the series should necessarily be equal to zero? (a) 10th (b) 8th (c) 1st (d) none of these

Answer 1

Answer:

(b) 8th

Step-by-step explanation:

let first term of A.P. be =a and common difference be =d,then

6th term + 15th term = (a+5d)+(a+14d) =2a+19d

7th tern+ 10term+12 term=(a+6d)+(a+9d)+(a+11d)=3a+26d

then according to question

2a+19d=3a+26d

⇒a+7d=0

which is 8th term (a+7d)

Answer 2

ANSWER

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

Then third term will be =a+2d

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

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

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

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

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

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

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

$= > a + 11d = 0$

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

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

HOPE IT'S HELPS YOU ❣️