Question

if the 3rd and the 9th terms of an Ap are 4 and -8 respectively which terms of this Ap is zero?
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Answer 1

Answer:

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Answer 2

Given:-

• 3rd term = 4
• 9th term = -8

To find:-

• Find term of an A.P. is zero ?

Solutions:-

The 3rd term of Ap is 4

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

=> 4 = a + (3 - 1)d

=> 4 = a + 2d .......(i)

The 9th term of Ap is -8.

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

=> -8 = a + (9 - 1)d

=> -8 = a + 8d .......(i)

Now, Subtracting Eq. (ii) and (i) we get,

${a} \: + \: {8d} \: \: = \: \: {-8} \\ {a} \: + \: {2d} \: \: = \: \: {4} \\ \underline{ - \: \: \: \: \: \: \: \: - \: \: \: \: \: \: \: \: = \: \: \: \: \: \: - \: \: \: \: \: \: \: \: \: } \\ \: \: \: \: \: \: \: \: {6d} \: \: \: \: \: \: \: \: = \: \: \: {-12}$

=> d = -12/6

=> d = -2

Now, putting the value of d in Eq. (i).

=> 4 = a + 2d

=> 4 = a + 2(-2)

=> 4 = a + (-4)

=> 4 = a - 4

=> a = -4 - 4

=> a = -8

Now,

• First term (a) = 8
• Common difference (d) = -2
• Last term (l) = 0

a_n = a + (n - 1)d

=> 8 + (n - 1)-2

=> 8 + 2n + 2

=> 10 + 2n

=> 2n = 10

=> n = 10/2

=> n = 5

Hence, 5th term of an A.P is 0.