Question

Find the difference of 8th term and 4th term of the A.P. : 4, 9, 13, ..., 254.

​

Answer 1

Answer:

$\large\star\:\:\boxed{a_8-a_4=20}\:\:\star$

Step-by-step explanation:

❈ Given :–

• Correct A.P. :- 4,9,14,...,254.
• where a=4
• d=a₂-a₁=9-4=5
• aₙ=254

❈ To Find :–

• Difference of a₈ and a₄ (a₈-a₄)

❈ Formula Applied :–

• aₙ=a+(n-1)d

❈ Solution :–

We have, a=4, d=5, aₙ=254.

aₙ=a+(n-1)d

Putting the above values in the formula :

254=4+(n-1)(5)

254-4=5n-5

250+5=5n

5n=255

$n=\frac{255}{5}$

$\boxed{n=51}$

☆ Now, we have to find a₈-a₄ :

⇒ [a+(8-1)d]-[a+(4-1)d]

⇒ [4+(7)(5)]-[4+(3)(5)]

⇒ (4+35)-(4+15)

⇒ 39-19

$\implies\boxed{a_8-a_4=20}$

∴ The difference of 8th term and 4th term of this A.P. is 20.

→ Additional Information about A.P. :-

Arithmetic Progression (A.P.) is a sequence of numbers such that the difference between the consecutive terms is constant (which is d the common difference).

Example :- 2,4,6,8,... is in an A.P. where common difference(d)=4-2=2.

Answer 2

Step-by-step explanation:

Answer:

\large\star\:\:\boxed{a_8-a_4=20}\:\:\star⋆

a

8

−a

4

=20

⋆

Step-by-step explanation:

❈ Given :–

Correct A.P. :- 4,9,14,...,254.

where a=4

d=a₂-a₁=9-4=5

aₙ=254

❈ To Find :–

Difference of a₈ and a₄ (a₈-a₄)

❈ Formula Applied :–

aₙ=a+(n-1)d

❈ Solution :–

We have, a=4, d=5, aₙ=254.

aₙ=a+(n-1)d

Putting the above values in the formula :

254=4+(n-1)(5)

254-4=5n-5

250+5=5n

5n=255

n=\frac{255}{5}n=

5

255

\boxed{n=51}

n=51

☆ Now, we have to find a₈-a₄ :

⇒ [a+(8-1)d]-[a+(4-1)d]

⇒ [4+(7)(5)]-[4+(3)(5)]

⇒ (4+35)-(4+15)

⇒ 39-19

\implies\boxed{a_8-a_4=20}⟹

a

8

−a

4

=20

∴ The difference of 8th term and 4th term of this A.P. is 20.

→ Additional Information about A.P. :-

Arithmetic Progression (A.P.) is a sequence of numbers such that the difference between the consecutive terms is constant (which is d the common difference).

Example :- 2,4,6,8,... is in an A.P. where common difference(d)=4-2=2.