The 5th term of an AP is 20 and the common difference is -2, find the first 4 terms
a+4d=20
a=20-4d
a=20-(-8)=28
a=28, d=-2
First four terms
a,a+d,a+2d,a+3d.......
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The sum of 2nd and 5th terms of an ap is 23 . the difference of 3rd term and 10th term is 21 . find to terms of the ap
To find the first 4 terms of an arithmetic progression (AP), we can use the formula:
aₙ = a₁ + (n - 1)d
where:
- aₙ represents the nth term of the AP,
- a₁ represents the first term of the AP,
- n represents the position of the term,
- d represents the common difference.
Given that the 5th term (a₅) is 20 and the common difference (d) is -2, we can substitute these values into the formula and solve for the first four terms.
Let's solve it step-by-step:
Step 1: Identify the values
a₅ = 20
d = -2
Step 2: Substitute the values into the formula
20 = a₁ + (5 - 1)(-2)
Step 3: Simplify the equation
20 = a₁ + 4(-2)
20 = a₁ - 8
Step 4: Isolate a₁
a₁ = 20 + 8
a₁ = 28
Now we know that the first term (a₁) of the AP is 28. To find the first four terms, we substitute this value into the formula and calculate the terms.
Step 5: Calculate the first four terms
Term 1: a₁ = 28
Term 2: a₂ = a₁ + d = 28 + (-2) = 26
Term 3: a₃ = a₁ + 2d = 28 + 2(-2) = 28 - 4 = 24
Term 4: a₄ = a₁ + 3d = 28 + 3(-2) = 28 - 6 = 22
So, the first four terms of the arithmetic progression are 28, 26, 24, and 22.
To find the first four terms of an arithmetic progression (AP), we need the 5th term and the common difference.
The formula for the nth term of an AP is given by:
aₙ = a₁ + (n - 1) * d
Where:
aₙ is the nth term of the AP
a₁ is the first term of the AP
n is the position of the term
d is the common difference
Given that the 5th term (a₅) is 20 and the common difference (d) is -2, we can substitute these values into the formula to solve for the first term (a₁) and the other terms.
a₅ = a₁ + (5 - 1) * (-2)
20 = a₁ + 4 * (-2)
20 = a₁ - 8
To isolate a₁, we add 8 to both sides of the equation:
20 + 8 = a₁ - 8 + 8
28 = a₁
So, the first term (a₁) is 28.
Now, using the formula for the nth term, we can find the first four terms:
a₁ = 28
a₂ = a₁ + (2 - 1) * (-2) = 28 + 1 * (-2) = 28 - 2 = 26
a₃ = a₁ + (3 - 1) * (-2) = 28 + 2 * (-2) = 28 - 4 = 24
a₄ = a₁ + (4 - 1) * (-2) = 28 + 3 * (-2) = 28 - 6 = 22
Therefore, the first four terms of the arithmetic progression are: 28, 26, 24, 22.