The 6th term in an arithmetic sequence is 74 and the 10th term is 62 , find the 50th term
a + 5d = 74
a + 9d = 62
-4d = 8
d = -2
a = 84
84 + 49(-2) = ?
To find the 50th term of an arithmetic sequence, we first need to find the common difference (d).
We are given that the 6th term is 74 and the 10th term is 62.
To find the common difference, we can use the formula for the nth term of an arithmetic sequence:
nth term = a + (n - 1)d
where a is the first term, n is the term number, and d is the common difference.
Let's use the given information to find the common difference:
For the 6th term, we have:
74 = a + (6 - 1)d
And for the 10th term, we have:
62 = a + (10 - 1)d
We now have two equations:
1. a + 5d = 74
2. a + 9d = 62
To solve this system of equations, we can subtract equation 1 from equation 2:
(a + 9d) - (a + 5d) = 62 - 74
This simplifies to:
4d = -12
Dividing both sides by 4, we get:
d = -12/4
d = -3
Now that we have the common difference (d = -3), we can go back to our formula and find the first term (a) using one of the equations above:
a + 5d = 74
Substituting the value of d, we have:
a + 5(-3) = 74
Simplifying, we get:
a - 15 = 74
Adding 15 to both sides, we get:
a = 89
Now we have the first term (a = 89) and the common difference (d = -3). We can use the formula for the nth term to find the 50th term:
nth term = a + (n - 1)d
Substituting the values, we have:
50th term = 89 + (50 - 1)(-3)
Calculating this expression gives us:
50th term = 89 + 49(-3)
Simplifying further:
50th term = 89 - 147
Finally, we get:
50th term = -58