Question

Which term of AP 5, 9, 13, 17, ... is 81?​

Answer 1

Given :

AP = 5, 9, 13, 17, ...

To Find :

• Which term is 81

Solution :

In the given AP, we have

• First term, a = 5
• Common difference, d = 9 - 5 = 4

Let it's nth term be 81.

$\sf : \implies T_{n} = 81$

Now, we know that,

$\large \underline{\boxed{\sf T_{n} = a + ( n - 1 ) d}}$

Now, by putting values,

$\sf : \implies 81 = 5 + ( n - 1 ) \times 4$

$\sf : \implies 81 = 5 + 4n - 4$

$\sf : \implies 81 = 1 + 4n$

$\sf : \implies 81 - 1 = 4n$

$\sf : \implies 80 = 4n$

$\sf : \implies 4n = 80$

$\sf : \implies n = \dfrac{\cancel{80}\: ^{20}}{\cancel{4}}$

$\sf : \implies n = 20$

$\large \underline{\boxed{\sf n = 20}}$

$\pink{ \sf Hence, \: the \: 20th \: term \: of \: AP\: is\: 81.}$

Answer 2

Question:-

1. Which term of AP 5, 9, 13, 17 is 81?

To find:-

• The term of 81

Given as:-

AP = 5, 9, 13, 17

Solution:-

$\rm \: a_n=a+(n-1)d \\ \rm{81=5+(n-1)(9-5)} \\ \rm{81-5=(n-1)4} \\ \rm\dfrac{76}{4}=n-1 =>n-1=19 \\ \rm{\fbox{Answer=>n \: = \: 20}}$

Hence, the 20th term of AP is 81