# Arithmetic Sequences Question

#### jaegermeister

##### New member
Hi,

I would appreciate some help on this problem. How would I find the “nth” term when I have its given value?

#### Subhotosh Khan

##### Super Moderator
Staff member
Hi,

I would appreciate some help on this problem. How would I find the “nth” term when I have its given value?
View attachment 29859
What will be the expression for the n'th term of an arithmetic sequence

when the first term is 'u1' and the common difference is 'd'?​

#### jaegermeister

##### New member
I mean how would I find which number in the sequence would have the value of 2. For example I know the first number in the sequence has the value 11.

#### Subhotosh Khan

##### Super Moderator
Staff member
I know what you mean. However, can you answer the question posed in repose #2?

What will be the expression for the n'th term of an arithmetic sequence

when the first term is 'u1' and the common difference is 'd'?

#### jaegermeister

##### New member
I’m not sure what you mean. For this question the first term, U1 was 11 and the common difference is -3.

#### Subhotosh Khan

##### Super Moderator
Staff member
What will be the expression for the n'th term of an arithmetic sequence

when the first term is 'u1' and the common difference is 'd'?
Putting aside the particular assignment, let us derive a general equation for the 'n' th term of AP.

For an Arithmetic Progression:

1 st. term = u1 + 0*d = u1 + (1-1)*d

2 nd. term = u1 + d = u1 + (2-1)*d

3 rd. term = u1 + 2*d = u1 + (3-1)*d

4 th. term = u1 + 3*d = u1 + (4-1)*d

5 th. term = ??

6 th. term = ??

#### jaegermeister

##### New member
5th term = u1 + 4*d = u1 + (5-1)*d

6th term = u1 + 5*d = u1 + (6-1)*d

#### Subhotosh Khan

##### Super Moderator
Staff member
5th term = u1 + 4*d = u1 + (5-1)*d

6th term = u1 + 5*d = u1 + (6-1)*d
Correct ...... now what will be the expression for the 'n' th term of the AP?

#### jaegermeister

##### New member
I don’t understand what you mean. Do you mean like n = u1 + (n – 1)d ?

#### Otis

##### Elite Member
I don’t understand what you mean. Do you mean like n = u1 + (n – 1)d ?
Yes, jaegermeister, but the right-hand side above represents the nth term (symbol un), not the index n itself.

un = u1 + (n - 1)(d)

You've been given values for the nth term un, the first term u1 and the common difference d. Substitute those numbers into the equation, and then solve for n.

u1 = 11
u2 = 11 - 3 = 8
u3 = 8 - 3 = 5
u4 = ?