Question

 If the common difference of an A.P. is 3, then find a20 – a15.​

Answer 1

Answer:

Answer = 15

Step-by-step explanation:

=> a20 - a15

=> a + 19d - a - 14d

=> 5d

=> 5x3

=> 15

Answer 2

☯ GiveN :

Common Difference of A.P (d) = 3

$\rule{200}{1}$

☯ To Find :

We have to find the value of a20 - a15.

$\rule{200}{1}$

☯ SolutioN :

We know that,

$\Large{\star{\boxed{\sf{A_n = a + (n - 1)d}}}}$

★ Putting Values ★

$\sf{\dashrightarrow A_{15} = a + (15 - 1)3} \\ \\ \sf{\dashrightarrow A_{15} = a + 14(3)} \\ \\ \sf{\dashrightarrow A_{15} = a + 42 ......(1)}$

$\rule{150}{2}$

↪ Similarly,

$\sf{\dashrightarrow A_{20} = a + (20 - 1)3} \\ \\ \sf{\dashrightarrow A_{15} = a + 19(3)} \\ \\ \sf{\dashrightarrow A_{15} = a + 57 ......(2)}$

$\rule{150}{2}$

From equation (1) and (2).

$\sf{\dashrightarrow A_{20} - A_{15} = a + 57 - (a + 57)} \\ \\ \sf{\dashrightarrow A_{20} - A_{15} = \cancel{a} + 57 \cancel{-a} - 42} \\ \\ \sf{\dashrightarrow A_{20} - A_{15} = 57 - 42} \\ \\ \sf{\dashrightarrow A_{20} - A_{15} = 15}$