Question

4th term of an arithmetic sequence is 17 and its 12th term is 49 . what is the common difference?​

Answer 1

Answer:

4

Step-by-step explanation:

Concept= Arithmetic Progression

Given= Fourth and 12th term of AP

To Find= The common difference

Explanation=

We have been the question as 4th term of an arithmetic sequence is 17 and its 12th term is 49 and we are asked to find the common difference.

The numbers in Arithmetic sequence or progression are as follows

a, a+d, a+2d ...... and so on

Where a is the first number while d is the common difference between them.

The nth term of Arithmetic Progression is written as aₙ= a+(n-1)d

So we have been given the 4th and 12th term as

a₄= 17 => a₄= a+(4-1)d=17

a₁₂= 49 => a₁₂= a+(12-1)d=49

So, 17= a+3d  ......(i)

     49= a+11d   .......(ii)

Therefore, solving simultaneously as a₁₂-a₄ we get

49= a+11d

17=  a+3d

-     -   -

(49-17) = (a-a) + (11d-3d)

32= 8d

d= 32/8 =4

Therefore the common difference is 4.

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