# Describe the difference between the meaning of n in the following two formulas: tn=a+(n−1)d and Sn=n2 [2a+(n−1)d]?

### 3 Answers

- Wayne DeguManLv 71 month ago
tₙ = a + (n - 1)d

Here, the n subscript means the specific nth term of the sequence

so, t₃ = a + 2d

i.e. the 3rd term has the value a + 2d

Sₙ = (n/2)[2a + (n - 1)d]

Here, the n subscript means the sum to n terms of the sequence

so, S₃ = (3/2)[2a + 2d] = 3(a + d)

Hence, the sum of the first 3 terms is 3(a + d)

i.e. S₃ = t₁ + t₂ + t₃

:)>

- davidLv 71 month ago
tn << I think that the n is a subscript .. it is a label

.. t(sub1) means the first t value

.. t(sub2) means the second t value /// etc

so t(subn) means the nth t value

==== on the right side of the 'equation' the 'n' is actually a variable that is replaced by a number and used to calculate the 't' value

sme thing for Sn >>> just a lable

but on the right it is a variable

... the 'n' in formulas of this type must be integers usually starting with 0 or 1 and continuing on as counting numbers to ...some value which may or may not be specified.

- RaymondLv 71 month ago
The "meaning" is the same. "n" marks the rank of a value, when you have a series.

n would normally be a counting number.

Where you have a series of values for something called "t", t7 (where n=7) would represent the 7th value in the series.

t = 2, 7, 12, 17, 22, 27, 32, 37, etc.

n being the rank, if you want the seventh value, you are asking for

t7 and you would use the formula, where you set n=7.

(in this example, it is the value 32, because I set a=2 and d=5)

The idea is the same for Sn

where S7 would ask for the 7th value of the "S" series.

To find it without having to write down the entire series, you simply use the function, where you would replace n by 7.

Sn = n^2 [2a + (n-1)d]

becomes

S7 = 7^2 [2a + 6d]