if 6 times the sixth term is equal to 15 times the fifteenth term ,find its 21st term
6(a+5d) = 15(a+14d)
6a + 30d = 15a + 210d
9a = -180d
a = -20d
a + 20d = -20d + 20d = 0
Very bad answers 😕 not satisfied
Yes. I agree with lakshmi
To solve this problem, we need to use the concept of an arithmetic sequence.
An arithmetic sequence is a sequence of numbers in which the difference between any two consecutive terms is constant. In this case, we are given that the sixth term and the fifteenth term are related by a certain ratio.
Let's represent the first term of the sequence as 'a' and the common difference as 'd'. Then, we can write the equation for the sixth term as:
a + 5d
Similarly, we can write the equation for the fifteenth term as:
a + 14d
According to the given information, 6 times the sixth term is equal to 15 times the fifteenth term. Mathematically, this can be expressed as:
6(a + 5d) = 15(a + 14d)
Now, let's simplify this equation:
6a + 30d = 15a + 210d
Next, let's group the 'a' terms and the 'd' terms separately:
30d - 210d = 15a - 6a
-180d = 9a
Finally, we can solve for 'd':
d = -9a/180
d = -a/20
We now know the value of the common difference 'd' in terms of 'a'.
To find the 21st term, we can substitute the values of 'a' and 'd' into the equation for the nth term of an arithmetic sequence:
21st term = a + (n - 1)d
Substituting 'a' and 'd' into the equation:
21st term = a + (21 - 1)(-a/20)
= a - 20a/20
= a - a
= 0
Therefore, the 21st term of the sequence is 0.