Question

5 th term of an arithmetic sequence is 17 and 17th term is 5 which term of the sequence is 0

Answer 1

EXPLANATION.

• GIVEN

5th term of an Ap = 17

17th term of an Ap = 5

Which term of the sequence is 0

=> Formula of Nth term of an Ap

=> An = a + ( n - 1 ) d

=> 5th term = 17

=> a + 4d = 17 .......(1)

17th term = 5

=> a + 16d = 5 .........(2)

From equation (1) and (2) we get,

=> -12d = 12

=> d = -1

put the value of d = -1 in equation (1)

we get,

=> a - 4 = 17

=> a = 21

Therefore,

First term of an Ap = a = 21

second term = a + d = 21 - 1 = 20

third term = a + 2d = 21 - 2 = 19

...........

...........

..........

22nd term = a + 21d = 21 - 21 = 0

Therefore,

22nd term of an Ap = 0

Answer 2

Given ,

5th and 17th term of an AP are 17 and 5

We know that , the nth term of an AP is

given by

$\boxed{ \sf{ a_{n} = a + (n - 1)d}}$

Thus ,

a + 4d = 17 --- (i)

and

a + 16d = 5 --- (ii)

Subtract eq (ii) from (i) , we get

a + 4d - (a + 16d) = 17 - 5

4d - 16d = 12

-12d = 12

d = -12/12

d = -1

Put the value of d = -1 in eq (i) , we get

a + 16(-1) = 5

a - 16 = 5

a = 21

Therefore ,

The first term and common difference of given AP are 21 and -1

Now ,

0 = 21 + (n - 1)(-1)

0 = 21 - n + 1

0 = 22 - n

n = 22

$\sf \therefore \underline{The \: 22th \: term \: of \: given \: AP \: is \: 0}$