Question

The sum of 6th element and the 14th element of an arthemetic Progression is-76. The sum of 8th and 16th element is -96. What is the value of 35th term

Answer 1

Step-by-step explanation:

6th element= a+5d

14th element= a+13d

Sum is given as -76

So, a+5d+a+13d=-76

2a+18d= 76

a+9d=38.........(i)

Given that the sum of 8th and 16th term is -96

8th term = a+7d

16th term = a+15d

Sum =-96

a+7d+a+15d=-96

2a+22d= -96

a+11d= -48.......(ii)

comparing equation (i) and (ii)

We have,

a=425

d= -43

So the 35th term will be,

a(n) = a+(n-1)d

a(35)=425+(35-1)*-43

a(35)= -1037

Therefore the 35th term is -1037

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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