Question

the nth term of a sequence is n squared +20
work out the first three terms of the sequence
how many terms in the sequence are less than 50

Answer 1

Step-by-step explanation:

1 x 1 + 20 =21

2×2+20=24

3×3+20=29

only 5 terms less than 50

Answer 2

Sequence can be arithmetic, geometric or none at all.

• The first three terms are 21, 24 and 29
• There are 5 terms in the sequence less than 50

The nth term of the sequence is given as:

$\mathbf{T_n = n^2 + 20}$

When n = 1, we have:

$\mathbf{T_1 = 1^2 + 20 = 1 + 20 = 21}$

When n = 2, we have:

$\mathbf{T_2 = 2^2 + 20 = 4 + 20 = 24}$

When n = 3, we have:

$\mathbf{T_3 = 3^2 + 20 = 9 + 20 = 29}$

So, the first three terms are 21, 24 and 29

Set n = 5.

So, we have:

$\mathbf{T_5 = 5^2 + 20 = 25 + 20 = 45}$

Set n = 6.

So, we have:

$\mathbf{T_6 = 6^2 + 20 = 36 + 20 = 56}$

T5 is less than 50, while T6 is greater than 60.

Hence, there are 5 terms in the sequence less than 50

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