A) 4.8
b) -9.9
Answer:
b) -9.9
Step-by-step explanation:
since its a negative its automatically smaller than any whole
hope this helps plz give brainliest
Step-by-step explanation:
To find the number of terms common to the two arithmetic progressions (APs), we can first determine the general terms of both sequences and then find their common terms.
The first AP has a common difference of 5, and the second AP also has a common difference of 5. We can write the general terms as:
First AP: a₁ = 2, a₂ = 2 + 5, a₃ = 2 + 2 * 5, ..., aₖ = 2 + (k - 1) * 5
Second AP: b₁ = 3, b₂ = 3 + 5, b₃ = 3 + 2 * 5, ..., bₖ = 3 + (k - 1) * 5
Now, we need to find when these two sequences are equal, i.e., aₖ = bₖ:
2 + (k - 1) * 5 = 3 + (k - 1) * 5
Simplifying this equation:
2 + 5k - 5 = 3 + 5k - 5
2 - 5 = 3 - 5
-3 = -3
The equation -3 = -3 is always true, which means that these two sequences are always equal for any value of k. Therefore, the number of terms common to the two APs is infinite, and the correct answer is:
d. None of these
The number of terms common to the two arithmetic progressions is 7.
To find the number of terms common to the two arithmetic progressions (A.P.s), we need to compare the terms of each A.P. and count the number of terms that are the same.
The first A.P. is 2, 5, 8, 11, ..., 98. The common difference between the terms is 3.
The second A.P. is 3, 8, 13, 18, ..., 198. The common difference between the terms is also 5.
To find the common terms, we can use the formula:
Term = First Term + (n - 1) * Common Difference
For the first A.P., we have:
First Term = 2
Common Difference = 3
For the second A.P., we have:
First Term = 3
Common Difference = 5
We need to find the values of 'n' that make the terms of both A.P.s the same. By substituting the values into the formula, we can solve for 'n' and calculate the number of common terms.
The number of terms common to the two A.P.s is 7. Therefore, the answer is option c.
Learn more about Arithmetic Progression here:
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