8 time the 8 term is equal to 12 times the twelve term.find the 20th term??
8(a+7d) = 12(a+11d)
8a+56d = 12a+132d
4a = -76d
a = -19d
So, there are many such sequences:
-19,-18,-17,-16,-15,-14,-13,-12,-11,-10,-9,-8
8(-12) = 12(-8)
38,36,34,32,30,28,26,24,22,20,18,16
8(24) = 12(16)
To solve this problem, we need to start by identifying the pattern of the given sequence.
Let's assume that the first term of the sequence is 'a' and the common difference between consecutive terms is 'd'.
According to the given information, the 8th term of the sequence is equal to 12 times the 12th term. Therefore, we can express this relationship as:
(a + (8-1)d) = 12 * (a + (12-1)d)
Simplifying this equation, we get:
(a + 7d) = 12 * (a + 11d)
Now, expand the equation further:
a + 7d = 12a + 132d
Subtracting 12a from both sides and rearranging the equation, we have:
7d - 132d = -11a
-125d = -11a
Dividing both sides of the equation by -11, we get:
d = a/11
This tells us that the common difference 'd' is equal to 'a' divided by 11.
To find the 20th term of the sequence, we can substitute these values back into the equation:
a + (20-1)d = a + 19(a/11)
Simplifying this equation, we get:
20a/11 = a + 19a/11
Multiplying both sides of the equation by 11 to eliminate the fraction, we have:
20a = 11a + 19a
Combining like terms, we get:
20a = 30a
Subtracting 30a from both sides, we get:
0 = 10a
Since the coefficient of 'a' is zero, it means that 'a' could be any value. Therefore, the 20th term of the sequence can be any value depending on the value of the first term 'a'.