How to find the last term of AP?

The nth term (an) of an arithmetic progression can be calculated as an = a + (n-1)d, where a is the first term and d is the common difference.
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What is the formula for the last term of an AP?

Given: The last term of AP refers to as l. Given that l = 20, d = -1, n = 17. We need to find a. By using l = a + (n – 1)d, we can find a.
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How do you find the end term of an AP?

Therefore, the nth term of an AP (an) with the first term “a” and common difference “d” is given by the formula: nth term of an AP, an = a+(n-1)d. (Note: The nth term of an AP (an) is sometimes called the general term of an AP, and also the last term in a sequence is sometimes denoted by “l”.)
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What is the formula to find term from end of AP?

nth term of an AP from the end

As a result, the nth term from the end equals the last term + (n–1)(–d). The nth term from the end is equal to l–(n–1)d.
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How do you find the first and last term of an AP?

Arithmetic Progression Formula (AP Formulas)
  1. Common difference of an AP: d = a2 - a1 = a3 - a2 = a4 - a3 = ... = an - a. n-1
  2. nth term of an AP: an = a + (n - 1)d.
  3. Sum of n terms of an AP: Sn = n/2 (2a + (n - 1) d) = n/2 (a + l), where l is the last term of the arithmetic progression.
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Example:Finding Last Term of Arithmetic Progression(AP)

Which term of the AP 3 8 13 18 is 78?

∴ 78 is 16th term of A.P: 3, 8,13, 18,...
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What is the 8th term from the end of the AP 5 8 11 38?

The given sequence is an Arithmetic Progression. ∴ The 8th term of the arithmetic sequence is 26.
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Is 184 a term of the AP 3 7 11 15?

Here, we can see that the value of \[n\] is not an integer. We know that the number of a term will never be a fraction. Therefore we can conclude that 184 is not a term in the given A.P.
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How to find the first term in AP?

Answer and Explanation:

an = a1 + d(n - 1), where a1 is the first term of the sequence, and d is the common difference of the sequence.
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How do you find the last 4th term of an AP?

  1. Step 1: Identify the AP and its properties. The given AP is: -11, -8, -5, ..., 49. ...
  2. Step 2: Reverse the AP. To find the 4th term from the end, we can reverse the sequence. ...
  3. Step 3: Determine the first term and common difference. ...
  4. Step 4: Calculate the 4th term from the start. ...
  5. Step 5: Substitute the values. ...
  6. Step 6: Conclusion.
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What is the nth term of an AP 9 13 17 21 25 nth?

Given AP: 9, 13, 17, 21, 25, … The formula to find the nth term of an AP is a + (n-1)d. = 4n + 5. Hence, the nth term of AP 9, 13, 17, 21, 25, … is 4n+5.
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How to find the last term in GP?

The general form of terms of a GP is a, ar, ar2, ar3, and so on. Here, a is the first term and r is the common ratio. The nth term from the end of the GP with the last term l and common ratio r = l/ [r(n – 1)]. The sum of infinite, i.e. the sum of a GP with infinite terms is S= a/(1 – r) such that 0 < r < 1.
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How to find the nth term?

Answer: The expression to calculate the nth term of an arithmetic sequence is an = a + (n - 1) d.
  1. 'a' is the first term of the AP.
  2. 'd' is the common difference.
  3. 'n' is the number of terms.
  4. 'an' is the nth term of the AP.
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What is the 20th term from the end of the AP 3 8 13 253?

The 20th term from the last term of the AP: 3, 8, 13, …, 253 is 158. Thus, the correct option is (D).
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How to find term from end of AP?

Assume that there are 'm' terms in an AP (Arithmetic Progression) in total whose first term is 'a' and the common difference is 'd'. Then the formula for the n term from the last of AP (its position from first would be (m-n+1) position) is: T = a + (m-n+1-1)d = a + (m - n) d.
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What is the last term of an AP called?

Answer: The nth term of AP. an = a + (n – 1) × d. Sum of n terms in AP. S = n/2[2a + (n − 1) × d] Sum of all terms in a finite AP with the last term as 'l'
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What is the 8th term from the end of AP 7 10 13 184?

8th term =184−(8−1)3=184−7×3=184−21=163.
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Is the nth term the last term?

We can also find the nth term from the end of the AP, Let us assume an AP where the first term is a and d is a common difference having m terms in it. Thus, the nth term from the end is (m-n+1)th term from the beginning. So, we can say a = a + (m -- n)d is the nth term from the last.
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How do you solve AP formula?

The sum of n terms of an AP can be found using one of the following formulas: S = n/2 (2a+(n−1)d) S = n/2 (a+a) Here, a = a = the first term, d = the common difference, n = number of terms, a = n term, S = the sum of the first n terms.
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How to find the general term of AP?

for the general or nth term of an arithmetic progression (AP) without using the AP formula Tn = a + (n − 1)d, where a is the first term, n is the number of terms and d is the common difference between successive terms.
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What is the formula to find the last term?

The general form of an Arithmetic Progression is a, a + d, a + 2d, a + 3d and so on. Thus nth term of an AP series is Tn = a + (n - 1) d, where Tn = nth term and a = first term. Here d = common difference = Tn - Tn-1. The sum of n terms is also equal to the formula where l is the last term.
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What is final term in arithmetic sequence?

The last term of the arithmetic sequence is indicated by the upper index. It is the number above in the sigma notation: . It is also the floating number when writing the terms in parentheses notation: ( a n ) n = 1 8 .
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