Question

Arthemetic sequence of 12th term is 6 and the 6th term is 12
A)find the common difference
B) find its first term
C) find its 18th term​

Answer 1

Given :-

• a₁₂ = 6

• a₆ = 12

To find :-

→ Common difference = d = ?

Solution :-

We know that

an = a + (n - 1)d

➝ a₁₂ = a + (12 - 1)d

➝ 6 = a + 11d ----- [Equation 1]

Similarly,

a₆ = a + (6 - 1)d

➝ 12 = a + 5d ----- [Equation 2]

Subtracting Equation 1 from 2,

[Equation 2 - Equation 1]

12 = a + 5d

{-} 6 = a + 11d

6 = -6d

➝ -6d = 6

➝ d = 6 ÷ -6

➝ d = -1

Therefore the common difference is -1

Know more:

We say that a set of numbers are in A.P if there a constant Common difference between the terms.

General form of an A.P → a, (a + d), (a + 2d), (a + 3d)...

There are 3 types of A.P. They are

1. Arithmetic Progression
2. Geometric Progression
3. Harmonic Progression

Answer 2

Answer:

difference between the terms =12-6=6

difference between the term position=6-12= -2

common difference =6÷-6 =-1