Question

An arithmetic sequence has a 7th term of 54 and a 13th term of 94.find the common difference

Answer 1

Answer:

Solving the above two equations we get,

a = 6

d = 4

Sum of n terms (Sn) is given by

Sn = (n/2)*(2*a + (n-1)*d)

=(n/2)*(12 + (n-1)*4)

= n*(6 + 2*n -2)

= 2*n*( n + 2 )

Answer

Answer 2

The common difference = 20/3

Given :

An arithmetic sequence has a 7th term of 54 and a 13th term of 94.

To find :

The common difference

Concept :

If in an arithmetic progression

First term = a

Common difference = d

Then nth term of the AP

= a + ( n - 1 )d

Solution :

Step 1 of 2 :

Form the equations

Let First term = a and Common difference = d

7th term = a + ( 7 - 1 )d = a + 6d

13th term = a + ( 13 - 1 )d = a + 12d

By the given condition

a + 6d = 54 - - - - - - (1)

a + 12d = 94 - - - - - (2)

Step 2 of 2 :

Find the common difference

Equation 2 - Equation 1 gives

6d = 40

⇒ d = 40/6

⇒ d = 20/3

Hence the required common difference = 20/3

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