Question

Q1
A gardener buys a plant that is 12cm in height. Each week after the plant grows 10cm. Note that
the plant is 12cm high at the beginning of the first week.
(a) What will be the height of the plant at the beginning of the 1st, 2nd. 3, and 4th week if it
follows the same pattern?
(b) For the above pattern, give your reasoning.
(c) Find the height of the plant at the beginning of the 10th week.
(d) Write the general term of the pattern of height.

whoever ans first will be marked as a brilianest​

Answer 1

Given:

The height of the plant that the gardener buys = 12 cm

Each week the plant grows by 10 cm

At the beginning of the first week, the height of the plant is 12 cm

To find:

a) What will be the height of the plant at the beginning of the 1st, 2nd. 3, and 4th week if it  follows the same pattern?

(b) For the above pattern, give your reasoning.

(c) Find the height of the plant at the beginning of the 10th week.

(d) Write the general term of the pattern of height.

Solution:

(a) Finding the height of the plant at the beginning of the 1st, 2nd, 3rd, and 4th week:

The plant is growing by 10 cm each week and also the same pattern is followed every week.

Therefore, we will find the height of the plant at the beginning of 1st, 2nd, 3rd and 4th week by following way:

The height of the plant at the beginning of the 1st week = 12 cm ... (given)

So,

The height of the plant at the beginning of the 2nd week = 12 + 10 = 22 cm

The height of the plant at the beginning of the 3rd week = 22 + 10 = 32 cm

The height of the plant at the beginning of the 4th week = 32 + 10 = 42 cm

(b) Finding the reason for the above pattern:

From the above pattern of calculation, we can say that it follows the general formula of arithmetic sequences i.e.,

$\boxed{\bold{t_n = a + (n -1)d}}$

here

a = first term = height of the plant at the beginning of the first week = 12 cm

n = no. of terms = week 1, week 2, week 3, week 4 ...... so on

d = common difference = plant grows each week by 10 cm

tₙ = $n^t^h$ term

(c) Finding the height of the plant at the beginning of the 10th week:

here

a = 12 cm

n = 10

d = 10 cm

Now, using the general formula of arithmetic sequences, we have

∴ t₁₀ = 12 + [(10 - 1)×10] = 12 + [9 × 10] = 12 + 90 = 102

Thus, the height of the plant at the beginning of the 10th week is 102 cm.

(d). Finding the general term of the pattern of height:

The general term of the pattern of the height of the plant is:

$\boxed{\boxed{\bold{t_n = a+(n-1)d}}}$

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