IF THE 6TH TERM OF A SERIES IS 24 AND THE COMMON DIFFERENCE IS 3 FIND THE SERIES
Comparing how easy this question is vs the other one you posted, my suspicion that you had a typo in your other post stands.
Here:
Since you are using the term "common difference" we can assume that your series is arithmetic.
a + 5d = 24, and d = 4, so
a + 20 = 24
a = 4
your series is
4 + 8 + 12 + 16 + 20 + 24 + ....
Hey mathhelper I think you misread the part where the question stated that D=3.
The solution for the following question will be like this:-
a+5d=24
since d=3 we write:-
a+5(3)=24
a+15=24
a=9.
The sequence for the following question will be:-
9, 12, 15, 18, 21, 24,...
To find the series given the 6th term and the common difference, you can use the formula for the nth term of an arithmetic series:
an = a1 + (n - 1)d,
Where:
an is the nth term
a1 is the first term
n is the number of terms
d is the common difference.
In this case, we know that:
a6 = 24,
d = 3.
Using the formula, we can substitute the given values:
24 = a1 + (6 - 1) × 3
Simplifying:
24 = a1 + 15
Subtracting 15 from both sides:
9 = a1
Therefore, the first term (a1) is 9.
To find the series, we can now substitute the values of a1 and d into the formula:
an = 9 + (n - 1) × 3
This will give us the general term for any term (an) in the series.
To find the series, we first need to determine the first term of the series.
Given that the sixth term is 24 and the common difference is 3, we can use the formula for the nth term of an arithmetic series:
an = a1 + (n - 1)d
where an is the nth term, a1 is the first term, n is the position of the term, and d is the common difference.
Plugging in the given values:
24 = a1 + (6 - 1)(3)
Simplifying:
24 = a1 + 15
Rearranging the equation:
a1 = 24 - 15
a1 = 9
So, the first term of the series is 9.
Now, we can find the series by adding the common difference (3) to each successive term.
The series would be: 9, 12, 15, 18, 21, 24, ...
Therefore, the series is 9, 12, 15, 18, 21, 24, ...