The fifth term of an AP is 20 and the common different is -2.Find the first four terms
just work backwards ...
20,22,24,26,28
In AP:
an = a1 + ( n - 1 ) d
In this case:
a5 = 20 , d = - 2
a5 = a1 + 4 d
20 = a1 + 4 ∙ ( - 2 )
20 = a1 - 8
Add 8 to both sides
28 = a1
a1 = 28
a2 = a1 + d = 28 + ( - 2 ) = 28 - 2 = 26
a3 = a1 + 2 d = 28 + 2 ∙ ( - 2 ) = 28 - 4 = 24
a4 = a1 + 3 d = 28 + 3 ∙ ( - 2 ) = 28 - 6 = 22
First four terms:
28 , 26 , 24 , 22
To find the first four terms of an arithmetic progression (AP), we need to use the given information about the fifth term and the common difference.
First, let's write down the general formula for the nth term of an arithmetic progression:
nth term = first term + (n-1) * common difference
From the given information, we know that the fifth term is 20 and the common difference is -2.
Let's substitute these values into the formula:
20 = first term + (5-1) * (-2)
20 = first term + 4*(-2)
Simplifying further:
20 = first term - 8
Now, let's isolate the first term:
first term = 20 + 8
first term = 28
So, the first term of the arithmetic progression is 28.
To find the next three terms, we can use the same formula and substitute the values into it:
2nd term = first term + (2-1) * common difference
3rd term = first term + (3-1) * common difference
4th term = first term + (4-1) * common difference
Substituting the values:
2nd term = 28 + 1*(-2)
2nd term = 28 - 2
2nd term = 26
3rd term = 28 + 2*(-2)
3rd term = 28 - 4
3rd term = 24
4th term = 28 + 3*(-2)
4th term = 28 - 6
4th term = 22
Therefore, the first four terms of the arithmetic progression are 28, 26, 24, and 22.