in an arithmetic progression the fifth term is 34 and the fifteenth term is 9.Which term in this progression is -6
10 differences are -25 ... so the common difference is -2.5
-6 is -15 from 9 ... -15 / -2.5 = 6 ... so -6 is the 21st term
Thank you
To find the term in the arithmetic progression that is -6, we need to determine the common difference of the progression first.
Let's assume that the first term of the arithmetic progression is "a" and the common difference is "d".
Given that the fifth term is 34, the formula for the nth term of an arithmetic progression can be used to calculate it:
nth term = a + (n - 1) * d
Substituting the values, we get:
34 = a + (5 - 1) * d
34 = a + 4d ... Equation 1
Similarly, given that the fifteenth term is 9, we can use the same formula to calculate it:
9 = a + (15 - 1) * d
9 = a + 14d ... Equation 2
Now, we have two equations with two unknowns (a and d). We can solve these equations simultaneously to determine the values.
We can start by subtracting Equation 2 from Equation 1 to eliminate "a":
34 - 9 = (a + 4d) - (a + 14d)
25 = -10d
Dividing both sides by -10:
d = -25/10 = -2.5
Now that we have the common difference, we can find the first term (a) by substituting the values into Equation 1:
34 = a + 4(-2.5)
34 = a - 10
a = 34 + 10 = 44
So, the arithmetic progression can be represented as: 44, 41.5, 39, 36.5, 34, ...
To find which term in this progression is -6, we can continue the pattern until we find it:
44, 41.5, 39, 36.5, 34, 31.5, 29, 26.5, 24, 21.5, 19, 16.5, 14, 11.5, 9
The term -6 does not exist in this arithmetic progression.