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.

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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