Question

If the 5th term of a AP is 12 and 8th term of AP is 16, then its common difference is *

2 points

3

4/3

2/3

3/4
please answer me fast
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Answer 1

Answer:

The common difference d = 4/3

Step-by-step explanation:  

Given that 5th term of AP = 12

                 8th term of AP = 16

In a AP or Arithmetic Progression  nth term  $T_{n} = a+ (n-1)d$

here $a$ is first term and $d$ is common difference

from given data  $T_{5} =$  $a +(5-1) d = 12$

                                ⇒ $a + 4d =12$ _ (1)

                           $T_{8}$  $= a + (8-1) = 16$

                                ⇒ $a +7d =16$ _ (2)

 equation (1) - equation (2) =  $a + 4d -( a+7d) = 12-16$    

                                            ⇒ $a+4d -a-7d = -4$  

                                            ⇒ $-3d = -4$

                                            ⇒  $d = \frac{4}{3}$  

Answer 2

Given:

The 5th term of an AP is 12 and the 8th term of the same AP is 16.

To Find:

The Common difference of the AP is?

Solution:

The given problem can be solved using the concepts of Arithmetic Progression.

1. The nth term of an AP with first term a, common difference d, and nth term Tn is given by the formula,

• Tn = a + (n-1)d

2. The 5th term of the AP is 12,

=> T5 = a + 4d = 12. ( Assume as equation 1 )

3. The 8th term of the AP is 16,

=> T8 = a + 7d = 16. ( Assume as equation 2 )

4. Solve equations 1 and 2 for values of a and d.

=> Subtract equation 1 from equation 2,

=> a + 7d - (a+4d) = 16 - 12,

=> a + 7d -a -4d = 4,

=> 3d = 4,

=> d = 4/3.

Therefore, the common difference of the given AP is 4/3. Option B is the correct answer.