Question

for an AP.t3=20and t4=24, find the common difference d
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Answer 1

Step-by-step explanation:

t3=20

t4=24

t4-t3=24-20

=4

d=4

Answer 2

Given:

In an arithmetic progression, the value of t3 is 20 and the value of t4 is 24.

To Find:

The value of the common difference d is?

Solution:

1. Consider an A.P having n terms with the first term a, common difference d. The nth term of the A.P is given by the formula,

=> nth term of an A.P = Tn = a + (n-1)d,

2. Use the above formula for the third and fourth terms,

=> t3 = a + 2d = 20 ( Assume as eqaution 1 ),

=> t4 = a + 3d = 24 ( Assume as equation 2 ).

3. Solved equations 1 and 2 for values of a and d,

=> Subtract equation 1 from equation 2,

=> ( a + 3d ) - ( a + 2d) = 24 -20,

=> a + 3d - a - 2d = 4,

=> d = 4.

4. Substitute the value of d in equation 1,

=> a + 8 = 20,

=> a = 12.

5. The A.P is 12, 16, 20, 24, 28, and so on.

The value of the common difference is 4.