Question

62%

Answer 1

Answer:

(a) $Sequence: -1, 1, 3$

(b) nth term: $T_n = 4+ 5n$

Step-by-step explanation:

Solving (a)

Given

$T_n = 2n - 3$

The first 3 terms.

When n = 1

$T_1 = 2*1 - 3$

$T_1 = 2 - 3$

$T_1 = -1$

When n = 2

$T_2 = 2*2 - 3$

$T_2 = 4 - 3$

$T_2 = 1$

When n = 3

$T_3 = 3*2 - 3$

$T_3 = 6 - 3$

$T_3= 3$

So, the first three terms are:

$Sequence: -1, 1, 3$

Solving (b)

Given

$Sequence: 9,14,19,24$

Required

The nth term

The sequence is arithmetic.

So, first calculate the common difference (d)

$d = 14 - 9$

$d = 5$

The nth term is then calculated as:

$T_n = a + (n - 1) * d$

Where

$a =First\ term$

So:

$a = 9$ and $d = 5$

$T_n = 9 + (n - 1) * 5$

$T_n = 9 + 5n - 5$

Collect like terms

$T_n = 9 - 5+ 5n$

$T_n = 4+ 5n$