Question

Find the first term and the common difference of the arithmetic sequence whose 6th term is 30 and 12th term

Answer 1

Answer:

Given :-

6th term = 30

12th term = 54

To Find :-

First term

Common difference

Solution :-

We know that

$\sf \: a_{n} = a + (n - 1)d$

For 6th term

$\sf \: 30 = a + (6 - 1)d$

$\sf \: 30 = a + 5d$

For 12th term

$\sf \: a_{n} = a + (n - 1)d$

$\sf \: 54 = a + (12 - 1)d$

$\sf \: 54 = a + 11d$

On subtracting both

$\sf \: 54 - 30 = a + 11d - (a + 5d)$

$\sf \: 54 - 30 = a + 11d - a - 5d$

$\sf \: 24 = 6d$

$\sf \: \dfrac{24}{6} = d$

$\sf \: 4 = d$

Now

Using 2

$\sf \: 54 = a + 11d$

$\sf \: 54 = a + 11(4)$

$\sf \: 54 = a + 44$

$\sf \: 54 - 44 = a$

$\sf \: 10 = a$

Answer 2

Answer:

• 10 and 4

Step-by-step explanation:

The first term is a, common difference is d.

The 6th term:

• a + 5d = 30

The 12th term:

• a + 11d = 54

Solve the system by elimination:

• 11d - 5d = 54 - 30
• 6d = 24
• d = 4

Find a:

• a + 5*4 = 30
• a + 20 = 30
• a = 10