If 3rd and 9th term of A.P are 4 and -8 respectively, then which term of its will be zero
in 6 terms, the value has gone from 4 to -8
0 is 1/3 of the distance between 4 and -8
so, you want the term 1/3 of the way from 3 to 9...
To find the term of the arithmetic progression (A.P.) that is equal to zero, we need to determine the common difference (d) of the A.P.
We are given that the 3rd term (a3) is 4 and the 9th term (a9) is -8. The general formula to find the nth term (an) of an A.P. is:
an = a1 + (n-1)d,
where a1 is the first term of the A.P. and n denotes the term number.
Using the given information, we can write two equations:
a3 = a1 + 2d = 4 -- Equation 1
a9 = a1 + 8d = -8 -- Equation 2
Next, we need to solve these equations simultaneously to find the values of a1 and d.
Subtracting Equation 1 from Equation 2, we eliminate a1:
a9 - a3 = (a1 + 8d) - (a1 + 2d)
-8 - 4 = 8d - 2d
-12 = 6d
Dividing both sides of the equation by 6, we find:
d = -2
Now that we have determined the common difference to be -2, we can find the term (n) that is equal to zero. We can use the formula for an A.P. term and set it equal to zero:
an = a1 + (n-1)d = 0
Substituting the values we know:
a1 + (n - 1)(-2) = 0
We can rearrange the equation and solve for n:
a1 - 2n + 2 = 0
-2n = -a1 - 2
n = (a1 + 2) / 2
To find the term that is equal to zero, we need to find the value of a1. Since we don't have that information, we cannot determine the specific term number that would be equal to zero.