What is the difference between n and tn in arithmetic progression ?

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Answer

Difference between n and tn in arithmetic progression

In an arithmetic progression (AP), the difference between any two consecutive terms is constant. This constant is known as the common difference (d). AP is represented as:

a, a + d, a + 2d, a + 3d, ...

where a is the first term of the AP and d is the common difference.

n in AP

n represents the number of terms in an arithmetic progression. It is usually denoted by a lowercase ‘n’.

For example, in the AP – 3, 6, 9, 12, 15, 18, 21, the value of n is 7 because there are 7 terms in the progression.

tn in AP

tn represents the nth term of an arithmetic progression. It is usually denoted by a lowercase ‘t’ with a subscript ‘n’.

For example, in the AP – 3, 6, 9, 12, 15, 18, 21, the value of t₅ is 15 because it is the 5th term in the progression.

Difference between n and tn

n represents the total number of terms in an AP, whereas tn represents the value of the nth term in an AP.

n is a whole number that gives the count of the terms in an AP, whereas tn is a specific value of a term in an AP.

n is used to calculate the sum of all the terms in an AP, whereas tn is used to find the value of a particular term in an AP.

n is denoted by lowercase ‘n’, whereas tn is denoted by lowercase ‘t’ with a subscript ‘n’.

Therefore, the main difference between n and tn in arithmetic progression is that n represents the total number of terms in an AP, whereas tn represents the value of the nth term in an AP.

Answer

An arithmetic progression, or AP, is a sequence where each new term after the first is obtained. by adding a constant d, called the common difference, to the preceding term. If the first term. of the sequence is a then the arithmetic progression is. a, a + d, a + 2d, a + 3d, ... where the n-th term is a + (n − 1)d.

If you look at the terms in your sequence you will see that the terms all decrease by 3 each time. This constant difference makes yoursequence an arithmetic sequence. There is a formula for finding the nth term of anarithmetic sequence: tn = a + (n-1)d where tnrepresents the nth term. a represents the first term.

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