28. In an AP, if the third term and seventh term are 4 and -8 respectively, then find which term
value is zero.
Answers
Correct Question :-
28. In an AP, if the third term and seventh term are 4 and 8 respectively, then find which term value is zero.
Solution :-
Third term () of an A.P. = 4
Seventh term () of an A.P. = 8
We know that -
= a + (n-1)d
where,
a = first term of an A.P.
n = number of terms of an A.P.
d = difference of consecutive terms of an A.P.
=> = a + (3-1)d
=> 4 = a + 2d
=> 4 - 2d = a ....i.)
=> = a + (7-1)d
=> 8 = a + 6d
[Substituting the value of a from eq. i.)]
=> 8 = 4 - 2d + 6d
=> 8 = 4 + 4d
=> 8 - 4 = 4d
=> 4 = 4d
=> d = 1
Finding the value of a by substituting the value of d in eq. i.)
=> a = 4 - 2d
=> a = 4 - 2 x 1
=> a = 4 - 2
=> a = 4 - 2
=> a = 2
According To the question -
= 0 and we have to find n.
Form the formula,
=> = a + (n-1)d
=> 0 = 2 + (n-1) x 1
=> 0 = 2 + n - 1
=> 0 = 1 + n
=> -1 = n
Here, Number of terms is -1. But n cannot be negative. So, 0 as a term does not exist in this A.P.