Question

The seventh term of an arithmetic sequence is 10.2 and the twelfth term is 17.7. What is the common difference of the arithmetic sequence? The common difference is

Answer 1

the common difference = 1.5

Explanation:

The seventh term of an arithmetic sequence is 10.2 and the twelfth term is 17.7

a7 = 10.2

a12= 17.7

Use the formula for nth term

`a_n= a_1+(n-1)d`

where 'd' is the common difference

n is the number of terms

a1 is the first term

`a_7= a_1+(7-1)d`

`10.2= a_1+6d` ---> equation 1

`a_12= a_1+(12-1)d`

`17.7= a_1+11d` -------------> equation 2

Subtract equation 2 - equation 1

`17.7= a_1+11d`

`10.2= a_1+6d`

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7.5 = 5d

divide by 5 on both sides

d= 1.5

So the common difference = 1.5

Answer 2

7 = 10.2
12 = 17.7
Let's take
d = 17.7 - 10.2/ 12 - 7
d = 7.5/ 5
d = 1.5
The common difference is 1.5