The arithmetic mean of 10 terms is 24, while arithmetic mean of last 8 term is 20. Find arithmetic mean of first two terms.
total of all 10 terms = 240
total of last 8 terms = 8(20) = 160
total of first 2 terms = 240-160 = 80
mean of first 2 terms = 80/2 = 40
To find the arithmetic mean of the first two terms, we will use the given information.
Let's denote the arithmetic mean of the first two terms as x.
We know that the arithmetic mean of 10 terms is 24. Therefore, the sum of the 10 terms is 10 * 24 = 240.
We also know that the arithmetic mean of the last 8 terms is 20. Therefore, the sum of the last 8 terms is 8 * 20 = 160.
To find the sum of the first two terms, we can subtract the sum of the last 8 terms from the sum of all 10 terms:
Sum of first two terms = Sum of all 10 terms - Sum of last 8 terms
Sum of first two terms = 240 - 160 = 80
Since the arithmetic mean is the sum of terms divided by the number of terms, we can calculate the arithmetic mean of the first two terms as:
Arithmetic mean of first two terms = Sum of first two terms / Number of terms
Arithmetic mean of first two terms = 80 / 2 = 40
Therefore, the arithmetic mean of the first two terms is 40.
To find the arithmetic mean of the first two terms, we need to first find the sum of all 10 terms.
Let's assume the sum of the 10 terms is S.
The arithmetic mean of 10 terms is given as 24, which means the sum of the 10 terms should be equal to 24 multiplied by 10, since the arithmetic mean is the sum divided by the number of terms. So we have:
S = 24 * 10
S = 240
Now, let's assume the sum of the last 8 terms is X.
The arithmetic mean of the last 8 terms is given as 20, which means the sum of the last 8 terms should be equal to 20 multiplied by 8. So we have:
X = 20 * 8
X = 160
Since the sum of all 10 terms (S) is equal to the sum of the last 8 terms (X) plus the sum of the first 2 terms, we can set up an equation:
S = X + Sum of first 2 terms
240 = 160 + Sum of first 2 terms
To find the arithmetic mean of the first two terms, we need to find their sum.
Subtracting 160 from both sides of the equation, we have:
240 - 160 = Sum of first 2 terms
80 = Sum of first 2 terms
To find the arithmetic mean, we divide the sum of the first two terms by 2 (since there are two terms):
Arithmetic mean of first two terms = Sum of first 2 terms / 2
Arithmetic mean of first two terms = 80 / 2
Arithmetic mean of first two terms = 40
Therefore, the arithmetic mean of the first two terms is 40.