Question

Solve it fast please

The 17th term of an arithmetic sequence is 5 and 5th term is 17. what is the 22nd term

Answer is 0 ​​

Answer 1

Step-by-step explanation:

the 17th term = a+16d = 5

the 5th term = a+4d = 17

find 22nd term?

solution

using simultaneous equation

a+16d=5

- a+4d =17

12d = -12

d = -1

a+16(-1) = 5

a-16 = 5

a= 5+16

a = 21

the 22nd term = a+21d

21 + 21(-1)

21-21 = 0

therefore the 22nd term is 0

Answer 2

Given : 17th term of an AP is 5 and it's 5th term is 17

To find : 22nd term of AP

Solution :

Inorder to find any term of AP, we must have the values of a ( first term ) and d ( common difference ).

We will use a shortcut trick to solve this question instead of elimination method to solve for a and d. Here's the trick !

Whenever we are given $A_n$ and $A_k$ terms of AP, then the common difference of the AP is given by,

$\rm Common\: difference=\dfrac{A_n-A_k}{n-k}$

We will use this to find the common difference.

We know that nth term of an AP is given by,

$\rm A_n = a+(n-1)d$

So,

$\implies\rm A_{17} = a+16d - - (1.)$

$\implies\rm A_{5} = a+4d$

Also,

$\rm Common\: difference=\dfrac{A_n-A_k}{n-k}$

$\rm Common\: difference=\dfrac{A_{17}-A_5}{17 - 5}$

$\rm Common\: difference=\dfrac{5 - 17}{17 - 5}$

$\rm Common\: difference=\dfrac{ - 12}{12}$

$\rm Common\: difference= - 1$

Now substitute this value of common difference in equation (1).

$\implies\rm A_{17} = a+16d$

$\implies\rm 5 = a+16( - 1)$

$\implies\rm 5 =a - 16$

$\implies\rm 5 + 16 =a$

$\implies\rm21 =a$

We are asked to find 22nd term

$\longrightarrow\rm A_{22} = a+21d$

$\longrightarrow\rm A_{22} = 21+21( - 1)$

$\longrightarrow\rm A_{22} = 21 - 21$

$\longrightarrow\rm A_{22} =0$

Hence the 22nd term of given AP is 0.