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a) The nth term of a sequence is 2n - 3
Work out the first three terms of the sequence.
[2]
b) Write down an expression for the nth term of the following sequence.
9, 14, 19,
[2]
24,
BH

Respuesta :

MrRoyal

Answer:

(a) [tex]Sequence: -1, 1, 3[/tex]

(b) nth term: [tex]T_n = 4+ 5n[/tex]

Step-by-step explanation:

Solving (a)

Given

[tex]T_n = 2n - 3[/tex]

The first 3 terms.

When n = 1

[tex]T_1 = 2*1 - 3[/tex]

[tex]T_1 = 2 - 3[/tex]

[tex]T_1 = -1[/tex]

When n = 2

[tex]T_2 = 2*2 - 3[/tex]

[tex]T_2 = 4 - 3[/tex]

[tex]T_2 = 1[/tex]

When n = 3

[tex]T_3 = 3*2 - 3[/tex]

[tex]T_3 = 6 - 3[/tex]

[tex]T_3= 3[/tex]

So, the first three terms are:

[tex]Sequence: -1, 1, 3[/tex]

Solving (b)

Given

[tex]Sequence: 9,14,19,24[/tex]

Required

The nth term

The sequence is arithmetic.

So, first calculate the common difference (d)

[tex]d = 14 - 9[/tex]

[tex]d = 5[/tex]

The nth term is then calculated as:

[tex]T_n = a + (n - 1) * d[/tex]

Where

[tex]a =First\ term[/tex]

So:

[tex]a = 9[/tex] and [tex]d = 5[/tex]

[tex]T_n = 9 + (n - 1) * 5[/tex]

[tex]T_n = 9 + 5n - 5[/tex]

Collect like terms

[tex]T_n = 9 - 5+ 5n[/tex]

[tex]T_n = 4+ 5n[/tex]