In an AP, if the third term and seventh term are 4 and 8 respectively, then find which term
value is zero.
Answers
Step-by-step explanation:
Given:-
In an AP, if the third term and seventh term are 4 and 8 respectively.
To find:-
Find which term value is zero ?
Solution:-
Third term of the given AP = 4
t3 = 4
a+2d = 4-------(1)
Seventh term of the given AP = 8
t7 = 8
a+6d = 8 ------(2)
On solving (1)&(2)
a+2d = 4
a+6d = 8
(-)
_________
0-4d = -4
_________
=>-4d = -4
=>4d = 4
=>d = 4/4
=>d = 1
Common difference of the AP = 1
On Substituting the value of d in (1)
=>a+2(1) = 4
=>a+2 = 4
=>a = 4-2
=>a = 2
First term of the AP = 2
Then the AP :2,3,4,5,6,7,8....
Let nth term of the AP will be zero
=>tn = 0
=>a+(n-1)d = 0
=>2+(n-1)(1) = 0
=>2+(n-1) = 0
=>2+n-1 = 0
=>n+1 = 0
=>n = -1
Number of terms = -1
Answer:-
n = -1 , but n can not be negative
So there is no such term in the given AP can not be equal to zero.
And also It is an increasing series (AP)
Check:-
The first term = 2
Common difference = 1
The AP : 2,3,4,5,6,7,8,...
Third term = 4
Seventh term = 8