Question

is - 150 is a term of AP 17,12, 7,2...

Answer 1

Here
initial term (a) = 17
common difference (d) = -5

Let a + (n-1)d= –150
if n is whole number then –150 is a term of the AP otherwise it isn't.

solving for n

17 + (n-1)(–5)= –150
(n-1)(–5) = –167
(n-1) = –167/–5 = 33.4
n= 33.4+1 =34.4

Since n is not a whole number –150 is not a term of the AP .


HOPE IT HELPS...... :-)

Answer 2

Hi !

First term =  a = 17

Common difference = d = -5

an = -150

an = a + [ n - 1] d

-150 = 17 + [ n - 1 ] -5

-150 - 17 = [n - 1 ] -5

-150 - 17 = ( n- 1) -5

-167 = (n - 1)-5

167/5 = n - 1

167/5 + 1 = n

167/5 + 5/5 = n

172/5 = n

n is not a natural  no:

Therefore , -150 is not a term of the A.P