MHB A problem on arithmetic progressions.

[mathlearn]

View attachment 5944

Okay, So far I have seen and know to find the common difference of arithmetic terms using the consecutive terms. But this progression looks different (Shake)

Find the common difference , Value of Z and the first term of it.

Many Thanks (Happy)

 

[Greg]

Since 42 is four terms after 22 we must have 22 + 4d = 42, where d is the common difference. Can you solve for d and use that value to complete the other questions?

 

[mathlearn]

Since 42 is four terms after 22 we must have 22 + 4d = 42, where d is the common difference. Can you solve for d and use that value to complete the other questions?

Using the equation 22 + 4d = 42; d = 5;

Correct?

Now is there another way to find this,My method was to add 3 times the common difference.

Z=42+(5*3)
Z=42+15
Z=42+15
Z=57

To find the first term of the sequence , using the formula

an = a1 + (n – 1)d
57 = a1 + (10 – 1)5
57 = a1 + 45
57-45=a1
12=a1

 

[Greg]

Your value for d is wrong but everything else looks correct.

 

[Greg]

I see you've edited your post. d = 5 is correct.

 

[mathlearn]

Thank you ;)

 

[Greg]

Using the equation 22 + 4d = 42; d = 5;

Correct?

Now is there another way to find this,My method was to add 3 times the common difference.

Z=42+(5*3)
Z=42+15
Z=42+15
Z=57

To find the first term of the sequence , using the formula

an = a1 + (n – 1)d
57 = a1 + (10 – 1)5
57 = a1 + 45
57-45=a1
12=a1

Well done! :)