Question

if the common difference of AP is 5then what is a18-a13

Answer 1

Here it is given that d = 5
a18 - a13
= a + 17d - (a + 12d)
= a + 17d - a - 12d
= 17d - 12d

Substituting 'd' by 5

= (17 × 5) - (12 × 5)
= 85 - 60
= 25

Therefore, a18 - a13 = 25

Answer 2

a₁₈ - a₁₃ = 25

Given :

The common difference of an AP is 5

To find :

The value of a₁₈ - a₁₃

Concept :

If in an arithmetic progression

First term = a

Common difference = d

Then nth term of the AP

= a + ( n - 1 )d

Solution :

Step 1 of 2 :

Find 18th term and 13th term

Let first term = a

Common Difference = d = 5

18th term = a₁₈ = a + (18 - 1)d = a + 17d

13th term = a₁₃ = a + (13 - 1)d = a + 12d

Step 2 of 2 :

Find the value of a₁₈ - a₁₃

a₁₈ - a₁₃

= 18th term - 13th term

= (a + 17d) - (a + 12d)

= a + 17d - a - 12d

= 5d

= 5 × 5

= 25

Hence the value of a₁₈ - a₁₃ = 25

━━━━━━━━━━━━━━━━

Learn more from Brainly :-

$1.$ If the middle term of a finite AP with 7 terms is 21 find the sum of all terms of the AP

https://brainly.in/question/30198388

2. find the 100th term of an AP whose nth term is 3n+1

https://brainly.in/question/22293445