Question

If the common difference of an is 5,then what is a18 - a13 ?
A) 5
B) 20
C) 25
D) 30 ​

Answer 1

Answer:

I think the answer is 20

Step-by-step explanation:

but I am not clear about it

Answer 2

A n s w e r

$\:\:$

G i v e n

$\:\:$

• Common difference of an AP is 5

$\:\:$

F i n d

$\:\:$

• a18 - a13

$\:\:$

S o l u t i o n

$\:\:$

We know that,

$\:\:$

➠ an = a + (n - 1)d ⚊⚊⚊⚊ ⓵

$\:\:$

Where,

$\:\:$

• an = nth term

• a = First term

• d = Common difference

• n = Number of terms

$\:\:$

For a18

$\:\:$

• an = a18

• a = a

• d = 5

• n = 18

$\:\:$

⟮ Putting the above values in ⓵ ⟯

$\:\:$

➜ an = a + (n - 1)d

$\:\:$

➜ a18 = a + (18 - 1)d

$\:\:$

➜ a18 = a + 17(d) ⚊⚊⚊⚊ ⓶

$\:\:$

For a13

$\:\:$

• an = a13

• a = a

• d = 5

• n = 13

$\:\:$

⟮ Putting the above values in ⓵ ⟯

$\:\:$

➜ an = a + (n - 1)d

$\:\:$

➜ a13 = a + (13 - 1)d

$\:\:$

➜ a13 = a + 12(d) ⚊⚊⚊⚊ ⓷

$\:\:$

Equation ⓶ - ⓷

$\:\:$

➜ a18 - a13 = a + 17(d) - [a + 12(d)]

$\:\:$

➜ a18 - a13 = a + 17(d) - a - 12(d)

$\:\:$

➜ a18 - a13 = 5d

$\:\:$

➜ a18 - a13 = 5(5)

$\:\:$

➨ a18 - a13 = 25

$\:\:$

• Hence option C) 25 is the correct answer

$\:\:$

═════════════════════════