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SVETLANKA909090 [29]
3 years ago
12

Pls solve this for me ryt now wai abeg

Mathematics
1 answer:
Alex777 [14]3 years ago
3 0

Answer:

x = 2

S_n = 63

Step-by-step explanation:

Given

a_1 = x + 1

a_2 = 4x -2

a_3 = 6x -3

a_n = 18

Solving (a): x

To do this, we make use of common difference (d)

d = a_2 - a_1

d = a_3 - a_2

So, we have:

a_3 - a_2 = a_2 - a_1

Substitute known values

(6x - 3) - (4x - 2) = (4x - 2) - (x + 1)

Remove brackets

6x - 3 - 4x + 2 = 4x - 2 - x - 1

Collect like terms

6x - 4x- 3  + 2 = 4x - x- 2  - 1

2x- 1 = 3x- 3

Collect like terms

2x - 3x = 1 - 3

-x = -2

x = 2

Solving (b): Sum of progression

First, we calculate the first term

a_1 = x + 1

a_1 = 2 + 1 = 3

Next, calculate d

d = a_2 - a_1

d = (4x - 2) - (x +1)

d = (4*2 - 2) - (2 +1)

d = 6 - 3 = 3

Next, we calculate n using:

a_n = a + (n - 1)d

Where:

a_n = 18

d = 3; a = 3

So:

18 = 3 +(n - 1) * 3

Subtract 3 from both sides

15 = (n - 1) * 3

Divide both sides by 3

5 = n - 1

Add 1 to both sides

6 = n

n = 6

The sum of the progression is:

S_n = \frac{n}{2} * [a + a_n]

So,, we have:

S_n = \frac{6}{2} * [3 + 18]

S_n = 3 * 21

S_n = 63

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