1. If the 4 term and first term of an AP are 9 and 21 respectively. Find common difference.
We know that the formula for the nth term of an AP is: an = a1 + (n-1)d.
We are given that the first term, a1, is 21.
We are also given that the 4th term, a4, is 9.
Using the formula, we can plug in these values and solve for d:
a4 = a1 + (4-1)d
9 = 21 + 3d
-12 = 3d
d = -4
Therefore, the common difference is -4.
What is the 5 ^ (th) term of 32 + 16 + 8
To find the 5th term of this sequence, we need to first determine the pattern of the sequence. We can write the terms of the sequence as:
a1 = 32
a2 = 16
a3 = 8
We can see that each term is half of the previous term. Therefore, the common ratio of this geometric sequence is 1/2.
Using this common ratio, we can find the 5th term, which is:
a5 = a1 * (r)^(n-1)
a5 = 32 * (1/2)^(5-1)
a5 = 32 * (1/2)^4
a5 = 32 * 1/16
a5 = 2
Therefore, the 5th term of the sequence is 2.
To find the common difference in an arithmetic progression (AP), you can use the formula:
an = a1 + (n-1)d
Where:
an is the nth term
a1 is the first term
n is the position of the term
d is the common difference
Here, the first term (a1) is given as 21, and the fourth term (a4) is given as 9.
Substituting these values into the formula, we get:
a4 = a1 + (4-1)d
9 = 21 + 3d
Simplifying the equation, we have:
-3d = -12
d = 4
Therefore, the common difference in this arithmetic progression is 4.