Question

If 2k+1, 4k and 4k+3 are three consecutive terms of an A.P then write the value of k.

Answer 1

Answer:

$\bigstar{\bold{The\:value\:of\:k=2}}$

Step-by-step explanation:

$\Large{\underline{\underline{\bf{Given:}}}}$

• 2k + 1 , 4k , 4k + 3 are three consecutive terms of an A.P

$\Large{\underline{\underline{\bf{To\:Find:}}}$

• The value of k

$\Large{\underline{\underline{\bf{Solution:}}}}$

→ Let a = 2k + 1, b = 4k, c = 4k + 3.

→ Since they are in A.P

  b = ( a + c ) /2

→ Substitute the datas,

  4k = ( 2k + 1 + 4k +3 )/2

  4k × 2 = 6k + 4

  8k = 6k + 4

  8k - 6k = 4

  2k = 4

    k = 4/2

    k = 2

$\boxed{\bold{The\:value\:of\:k=2}}$

$\Large{\underline{\underline{\bf{Verification:}}}}$

→ The first term of the A.P = a = 2k + 1

→ Substitute the value of k

  2 × 2 + 1 = 4 + 1 = 5

→ The second term of the A.P = b = 4k

→ Substitute the value of k

  4k = 4 × 2 = 8

→ The third term of the A.P = c = 4k + 3

→ Substitute value of k

  4k + 3 = 4 × 2 + 3 = 8 + 3 = 11

→ For three numbers to be in an A.P the common difference between them should be same, that is

 4k + 3 - 4k = 4k = 2k + 1

→ Substitute the values,

  11 - 8 = 8 - 5

        3 = 3

→ Hence the common difference is 3 and is same throughout. Therefore the numbers are in A.P

→ Hence verified.

Answer 2

Answer:

\bigstar{\bold{The\:value\:of\:k=2}}★Thevalueofk=2

Step-by-step explanation:

\Large{\underline{\underline{\bf{Given:}}}}

Given:

2k + 1 , 4k , 4k + 3 are three consecutive terms of an A.P

\Large{\underline{\underline{\bf{To\:Find:}}}

The value of k

\Large{\underline{\underline{\bf{Solution:}}}}

Solution:

→ Let a = 2k + 1, b = 4k, c = 4k + 3.

→ Since they are in A.P

b = ( a + c ) /2

→ Substitute the datas,

4k = ( 2k + 1 + 4k +3 )/2

4k × 2 = 6k + 4

8k = 6k + 4

8k - 6k = 4

2k = 4

k = 4/2

k = 2

\boxed{\bold{The\:value\:of\:k=2}}

Thevalueofk=2

\Large{\underline{\underline{\bf{Verification:}}}}

Verification:

→ The first term of the A.P = a = 2k + 1

→ Substitute the value of k

2 × 2 + 1 = 4 + 1 = 5

→ The second term of the A.P = b = 4k

→ Substitute the value of k

4k = 4 × 2 = 8

→ The third term of the A.P = c = 4k + 3

→ Substitute value of k

4k + 3 = 4 × 2 + 3 = 8 + 3 = 11

→ For three numbers to be in an A.P the common difference between them should be same, that is

4k + 3 - 4k = 4k = 2k + 1

→ Substitute the values,

11 - 8 = 8 - 5

3 = 3

→ Hence the common difference is 3 and is same throughout. Therefore the numbers are in A.P

→ Hence verified.