Question

The sum of 4th and 8th term of an arithmetic progression is 24. The value of 2nd term is 4

Find the value of d

Answer 1

Answer:

Common difference (d) = 2

Step-by-step explanation:

ATQ, The sum of the 4th and 8th term of an AP is 24.

⇒ a₄ + a₈ = 24.

(Here a₄ stands for the 4th term of the AP & a₈ stands for the 8th term of the ap)

ATQ, The second term is 4.

⇒ a₂ = 4

Using a$\sf _{n}$ = a + (n - 1)d we get,

⇒ a + (2 - 1)d = 4

⇒ a + (1)d = 4

⇒ a + d = 4 → Eq(1)

We know that,

⇒ a₄ + a₈ = 24.

⇒ a + 3d + a + 7d = 24

⇒ 2a + 10d = 24

⇒ 2(a + 5d) = 24

⇒ a + 5d = 24/2

⇒ a + 5d = 12 → Eq(2)

Subtracting Eq(1) from Eq(2) we get,

$\sf \ \ \ \ a \ \ + \ 5d = \ 12\\_{(-)} \ \ \ \ _{(-)} \ \ \ \ \ _{(-)}\\\sf {\ \ \ \ a \ \ + \ \ d = \ \ \ 4}\\\rule{80}{1}\\\sf {\ \ \ \ \ \ \ \ \ \ \ \ 4d = 8}\\ \\\sf {\ \ \ \ \ \ \ \ \ \ \ \ \ d = \dfrac{8}{4} }\\ \\\sf {\ \ \ \ \ \ \ \ \ \ \ \ \ d = 2}$

Therefore, the value of d is 2.

$\rule{150}{1}$

Verifying the answer:

(Isn't required unless it's asked in the question)

⇒ a₄ + a₈ = 24.

⇒ a + 3d + a + 7d = 24.

⇒ 2a + 10d = 24

⇒ 2a + 10(2) = 24

⇒ 2a + 20 = 24

⇒ 2a = 24 - 20

⇒ 2a = 4

⇒ a = 2

ATQ, 2nd term is 4.

⇒ a₂ = 4

⇒ a + d = 4

⇒ 2 + 2 = 4

⇒ 4 = 4

LHS = RHS

Hence the answer is correct.

Answer 2

Let first term be a and common difference be d .

Sum of $4^{th}$ and $8^{th}$ term is 24 .

$4^{th}$ term = a + 3d

$8^{th}$ term = a + 7d

$4^{th}$ term + $8^{th}$ term = 24

→ a + 3d + a + 7d =  24

→ 2a + 10d = 24

→ a + 5d = 12           ........... (1)

$2^{nd}$ term = 4

→ a + ( 2-1 )d = 4

→ a + d = 4                ............ (2)

Eq (1) - Eq (2)

→ 4d = 8

→ d = 2

Common difference = 2

HOPE IT HELPS U ............