QUESTION
If the 3rd and the 9th terms of an A.P. are 4 and − 8 respectively, then which term of this A.P is zero
Answers
Step-by-step explanation:
3rd term =a+(n-1)d
4= a+2d (1)
9th term =a+(n-1)d
-8= a+8d (2)
subtract eq (1) from eq (2)
4-(-8)= a+8d-(a+2d)
12=a+8d-a-2d
12=6d
-2=d
putting the value of d in eq (1)
4=a+2(-2)
4=a-4
4+4=a
8=a
0=a+(n-1)d
0=8+(n-1)(-2)
-8=(n-1)(-2)
-8/-2= n-1
4+1=n
5=n
hence, 5th term of the A.P. is zero
Answer:
The fifth term of the AP is zero.
Step-by-step-explanation:
We have given that,
Third term of an AP ( t₃ ) = 4
Ninth term of an AP ( t₉ ) = - 8
We have to find the term of the AP which is zero.
Now, we know that,
tₙ = a + ( n - 1 ) * d - - - [ Formula ]
⇒ t₃ = a + ( 3 - 1 ) * d
⇒ 4 = a + 2 * d - - - [ Given ]
⇒ 4 = a + 2d
⇒ a + 2d = 4
⇒ a = 4 - 2d - - - ( 1 )
Now,
tₙ = a + ( n - 1 ) * d - - - [ Formula ]
⇒ t₉ = a + ( 9 - 1 ) * d
⇒ - 8 = a + 8 * d - - - [ Given ]
⇒ - 8 = a + 8d
⇒ - 8 = ( 4 - 2d ) + 8d - - - [ From ( 1 ) ]
⇒ - 8 = 4 - 2d + 8d
⇒ - 8 - 4 = 6d
⇒ - 12 = 6d
⇒ d = - 12 ÷ 6
⇒ d = - 2
Now, by substituting d = - 2 in equation ( 1 ), we get,
a = 4 - 2d - - - ( 1 )
⇒ a = 4 - 2 * ( - 2 )
⇒ a = 4 + 4
⇒ a = 8
Now,
tₙ = a + ( n - 1 ) * d - - - [ Formula ]
⇒ 0 = 8 + ( n - 1 ) * ( - 2 )
⇒ 8 + ( n - 1 ) * ( - 2 ) = 0
⇒ 8 + ( - 2n ) + 2 = 0
⇒ 8 - 2n + 2 = 0
⇒ 8 + 2 - 2n = 0
⇒ 10 - 2n = 0
⇒ 10 = 2n
⇒ n = 10 ÷ 2
⇒ n = 5
∴ The fifth term of the AP is zero.