Question

What is the common difference of the AP  

             11, −1, −13, −25, . . . ? ​

Answer 1

The common difference in the arithmetic progression 11, −1, −13, −25, . . . is - 12

Given :

The arithmetic progression 11, −1, −13, −25, . . .

To find :

The common difference in the arithmetic progression

Solution :

Step 1 of 2 :

Write down the given arithmetic progression

The arithmetic progression is 11, −1, −13, −25, . . .

Step 2 of 2 :

Find common difference

We know that for a given arithmetic progression Common difference is the difference between two consecutive terms in the arithmetic progression

First term = a₁ = 11

Second term = a₂ = - 1

Third term = a₃ = - 13

a₂ - a₁ = - 1 - 11 = - 12

a₃ - a₂ = - 13 - (- 1) = - 13 + 1 = - 12

The required common difference

= 2nd term - 1st term

= - 12

Hence common difference in the arithmetic progression 11, −1, −13, −25, . . . is - 12

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Learn more from Brainly :-

$1.$ If for an A.P., S15= 147 and s14=123 find t 15

(A) 24 (B) 23 (C) 47 (D) 46

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2. Insert there arithmetic means between -20 and 4

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Answer 2

Concept Introduction: Arithmetic Progression is a type of progression in which the difference between the two numbers is constant

Given:

We have been Given: AP of the numbers,

$11 \: - 1 \: - 13 \: - 25.............$

To Find:

We have to Find: Common Difference between the Numbers.

Solution:

According to the problem, the common difference between the Numbers can found by subtracting each number from other, i.e.,

$a2 - a1 \: or \: a4 - a3$

therefore, doing as per the formula,

$a2 - a1 = - 1 - 11 = - 12 \\ a4 - a3 = - 25 - ( - 13) = - 12$

hence, the common difference between the Numbers is

$- 12$

Final Answer: The Common Difference between the Numbers is

$- 12$

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