Question

Pls help me CLASS 10 MATHS

Answer 1

Question:

The common difference of an AP is 5. The difference of 18th and 13th term is?

Answer:

$\bigstar{\bold{Difference\:=\:25}}$

Step-by-step explanation:

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

• Common difference (d) = 5

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

• Difference between the 18th and 13th terms

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

→ The 13th term of the AP = a₁₃ = a + 12d --------- equation 1

→ The 18th term of the AP = a₁₈ = a + 17d ----equation 2

→ Subtracting equation 2 from equation 1 gives us the difference between the 18th and 13th terms

  a₁₈ - a₁₃ = a + 17d - (a + 12d)

  a₁₈ - a₁₃ = a + 17d - a - 12 d

  a₁₈ - a₁₃ = 17d - 12 d

  a₁₈ - a₁₃ = 5d

→ Substituting the value of d from the given datas

   a₁₈ - a₁₃ = 5 × 5

   a₁₈ - a₁₃ = 25

$\boxed{\bold{Difference\:=\:25}}$

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

→ An AP is a series of numbers where the difference between any two consecutive terms is a constant.

→ Some formulae in AP

• $d\:=\:\dfrac{a_m\:-\:a_n}{m\:-\:n}$

• $a_n\:=\:a_1\:+\:(n-1)d$

• $S_n\:=\:\dfrac{n}{2} (a_1\:+\:a_n)$