# Nth termA sequence of numbers is shown: 2, 9, 16, 23, 30 ... ...(a) Find an expression for the nth term of the sequence. (b) Find the 100th term in the sequence. Please help!! Thanks for your answers. Much appreciated for your help.

1 answer

###### Question:

nth term

A sequence of numbers is shown: 2, 9, 16, 23, 30 ... ...

(a) Find an expression for the nth term of the sequence.

(b) Find the 100th term in the sequence.

Please help!! Thanks for your answers. Much appreciated for your help.

A sequence of numbers is shown: 2, 9, 16, 23, 30 ... ...

(a) Find an expression for the nth term of the sequence.

(b) Find the 100th term in the sequence.

Please help!! Thanks for your answers. Much appreciated for your help.

## Answers

So, we have a common difference of 7 (9 - 2 = 16 - 9 is true)For an arithmetic sequence, we have a generalised form:[tex]a_n = a_1 + (n - 1)d[/tex], where [tex]a_1[/tex] is the first term, n is the nth place, and d is the common difference.Now, to find the nth term, we substitute n as n to get:[tex]a_n = 2 + 7(n - 1)[/tex]Hence, to find the 100th term, we substitute n as 100 to get:[tex]a_100 = 2 + 7(100 - 1)[/tex][tex]= 2 + 7(99)[/tex][tex]= 2 + 693[/tex][tex]= 695[/tex]Thus, the 100th term is 695.

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