In an arithmetic sequence, the first term, a1, is equal to 5 , and the third term, a3, is equal to 9 . Which number represents the common difference of the arithmetic sequence?d=2d=3d=4d=5
Q. In an arithmetic sequence, the first term, a1, is equal to 5 , and the third term, a3, is equal to 9 . Which number represents the common difference of the arithmetic sequence?d=2d=3d=4d=5
Identify Given Terms: Identify the given terms in the arithmetic sequence.We are given the first term a1 and the third term a3 of the arithmetic sequence.a1=5a3=9
Use Formula for nth Term: Use the formula for the nth term of an arithmetic sequence to find the common difference.The formula for the nth term of an arithmetic sequence is:an=a1+(n−1)dwhere an is the nth term, a1 is the first term, d is the common difference, and n is the term number.
Plug Values and Find d: Plug the values of a1 and a3 into the formula to find d. We know that a3=a1+2d (since the third term is two terms away from the first term). So, 9=5+2d
Solve for d: Solve for d.Subtract 5 from both sides of the equation:9−5=2d4=2dNow, divide both sides by 2 to find d:d=24d=2