Question 831708: The 11th term of an arthmetric sequence is 57 and the sum of the first and fourth terms is 29. Determine the first 3 terms of the sequence
Answer by hovuquocan1997(83) (Show Source): You can put this solution on YOUR website! You have a formula to find any term in a arithmetic sequence and it is
Term = a + d(n - 1)
in which a is the first term and d is the difference between the terms, and n is the number of the term
ok so we have 11th term is 57, the equation will be
57 = a + d(11-1)
a + 10d = 57
That's the first equation
Now we move to the second one
We have First term is just "a"
and fourth term is a+d(4-1) = a + 3d
We have the sum of first and fourth terms is 29, that means a + a + 3d = 29
2a + 3d = 29
That's the second equation, now we have a system of 2 equations to solve for a, d
Solve: We'll use substitution. After moving 10*d to the right, we get: , or . Substitute that
into another equation: and simplify: So, we know that d=5. Since , a=7.
Answer: .
Now you know that a = 7, meaning that the first term is 7
d is 5, so the second term is 12, and the third term is 17
So the answer is 7, 12, 17
TA-DAH
:D