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Two APs have the same common difference. The first term of one of these is -1 and that of the other is -8. Then the difference between their 4th terms is
- a)-1
- b)-8
- c)7
- d)-9
Correct answer is option 'C'. Can you explain this answer?
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Two APs have the same common difference. The first term of one of thes...
a4 - b4 = (a1 + 3d) - (b1 + 3d)
= a1 b1 = - 1 - (-8) = 7
= a1 b1 = - 1 - (-8) = 7
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Two APs have the same common difference. The first term of one of thes...
To find the difference between the 4th terms of two arithmetic progressions (APs) with the same common difference, we need to determine the formulas for the two APs and then calculate the difference.
Given:
- The first term of one AP is -1.
- The first term of the other AP is -8.
- Both APs have the same common difference.
Finding the formulas for the two APs:
Let's assume the common difference is 'd'.
The formula for the first AP is:
a₁ = -1 (first term of the first AP)
a₄ = ?
d = ?
The formula for the second AP is:
a₁ = -8 (first term of the second AP)
a₄ = ?
d = ?
Using the formula for the nth term of an AP, which is given by:
aₙ = a₁ + (n - 1)d
We can substitute the given values into the formulas to find the values of a₄ for both APs.
For the first AP:
a₄ = -1 + (4 - 1)d
= -1 + 3d
For the second AP:
a₄ = -8 + (4 - 1)d
= -8 + 3d
Calculating the difference between the 4th terms:
To find the difference between the 4th terms, we subtract the value of the second AP from the value of the first AP:
Difference = (a₄ of first AP) - (a₄ of second AP)
= (-1 + 3d) - (-8 + 3d)
= -1 + 3d + 8 - 3d
= 7
Therefore, the difference between the 4th terms of the two APs is 7, which corresponds to option C.
Given:
- The first term of one AP is -1.
- The first term of the other AP is -8.
- Both APs have the same common difference.
Finding the formulas for the two APs:
Let's assume the common difference is 'd'.
The formula for the first AP is:
a₁ = -1 (first term of the first AP)
a₄ = ?
d = ?
The formula for the second AP is:
a₁ = -8 (first term of the second AP)
a₄ = ?
d = ?
Using the formula for the nth term of an AP, which is given by:
aₙ = a₁ + (n - 1)d
We can substitute the given values into the formulas to find the values of a₄ for both APs.
For the first AP:
a₄ = -1 + (4 - 1)d
= -1 + 3d
For the second AP:
a₄ = -8 + (4 - 1)d
= -8 + 3d
Calculating the difference between the 4th terms:
To find the difference between the 4th terms, we subtract the value of the second AP from the value of the first AP:
Difference = (a₄ of first AP) - (a₄ of second AP)
= (-1 + 3d) - (-8 + 3d)
= -1 + 3d + 8 - 3d
= 7
Therefore, the difference between the 4th terms of the two APs is 7, which corresponds to option C.
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Two APs have the same common difference. The first term of one of these is -1 and that of the other is -8. Then the difference between their 4th terms isa)-1b)-8c)7d)-9Correct answer is option 'C'. Can you explain this answer?
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