Question

if the 3rd and the 9th terms of an ap are 4 and -8 respectively which term of this ap is 0

Answer 1

Answer:

Let the first and common difference be a and d.

Step-by-step explanation:

a3=a+2d

a+2d=4......1

a9=a+8d

a+8d=-8.....2

subtract 2 from 1 we get

a+2d=4

a+8d=-8

_. _. +

-6d=-4

d=2/3

putting the value of d in 1

a+2d=4

a+2×2/3=4

a+4/3=4

a=4-4/3

a=(12-4)/3

a=8/3

Answer 2

Given:-

• The 3rd and the 9th terms of an ap are 4 and -8.

To find:-

• Find the nth term...?

Solutions:-

• The 3rd term of Ap is 4.
• The 9th term of Ap is -8.

we know that;

The 3rd term of Ap is 4.

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

=> a3 = a + (3 - 1)d

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

The 9th term of Ap is -8.

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

=> a9 = a + (9 - 1)d

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

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

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

=> d = -12/6

=> y = - 2

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

=> a + 2d = 4

=> a + 2(-2) = 4

=> a - 4 = 4

=> a = 4 + 4

=> a = 8

So,

Let nth term of an Ap be zero.

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

=> 0 = 8 + (n - 1) (-2)

=> 0 = 8 - 2n + 2

=> 0 = - 2n + 10

=> 2n = 10

=> n = 10/2

=> n = 5

Hence the 5th term of Ap is 0.