Question

4,a,b,28 are in A. p then the value of 'b'is a) 20 b) 19 c) 23 d) 12​

Answer 1

Given that:

• The terms of an AP: 4, a, b, 28

To Find:

• The value of b.

We have:

• a = 4
• l = 28
• n = 4

We know that:

• aₙ = a + (n - 1)d
• Sₙ = n{2a + (n - 1)d}/2 ____(i)
• Sₙ = n(a + l)/2 ____(ii)

Where,

• aₙ = nth term
• Sₙ = Sum of nth term
• a = First term
• n = Number of terms
• d = Common difference
• l = Last term

Comparing eqⁿ (i) and eq (ii):

⟶ n{2a + (n - 1)d}/2 = n(a + l)/2

Cancelling common terms.

⟶ {2a + (n - 1)d} = (a + l)

Substituting the values.

⟶ {2 × 4 + (4 - 1)d} = (4 + 28)

⟶ 8 + 3d = 32

⟶ 3d = 32 - 8

⟶ 3d = 24

⟶ d = 24/3

⟶ d = 8

Finding the value of b:

⟶ b = a₃

⟶ b = a + (3 - 1)d

⟶ b = a + 2d

⟶ b = 4 + 2× 8

⟶ b = 4 + 16

⟶ b = 20

Hence,

• The value of b is a) 20.

Answer 2

a) 20

Step-by-step explanation:

Q.

4, a, b, 28 are in A.P. then the value of b is

a) 20

b) 19

c) 23

d) 12

.

Solution -

We can see that

a = 4

a4 = 28

28 is 4th term

we know that,

nth term = a + (n - 1)d

4th term = 4 + (4-1)d

=> 28 = 4 + 3d

=> 28-4 = 3d

=> 24 = 3d

=> 24/3 = d

=> 8 = d

=> d = 8

Hence common difference is 8

Now,

b is 3rd term,

nth term = a + (n - 1)d

=> 3rd term = 4 + (3-1)8

=> 3rd term = 4 + 2(8)

=> 3rd term = 4 + 16 = 20

Hence 3rd term is 20 means value of b is 20.

Note :-

• a = first term
• n = nth term
• d = common difference

hope it helps.