In an arithmetic progression, if the 2nd term is 10 and the 4th term is 14, what

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Question: In an arithmetic progression, if the 2nd term is 10 and the 4th term is 14, what is the first term? (2023)

Options:

Correct Answer: 8

Exam Year: 2023

Solution:

Let the first term be a and the common difference be d. From the equations a + d = 10 and a + 3d = 14, we can solve for a and find it to be 8.

In an arithmetic progression, if the 2nd term is 10 and the 4th term is 14, what is the first term? (2023)

In an arithmetic progression, if the 2nd term is 10 and the 4th term is 14, what is the first term? (2023)

Step 1: Identify the first term as 'a' and the common difference as 'd'.
Step 2: Write the equation for the 2nd term: a + d = 10.
Step 3: Write the equation for the 4th term: a + 3d = 14.
Step 4: Now you have two equations: a + d = 10 and a + 3d = 14.
Step 5: From the first equation (a + d = 10), you can express 'd' as d = 10 - a.
Step 6: Substitute 'd' in the second equation (a + 3d = 14): a + 3(10 - a) = 14.
Step 7: Simplify the equation: a + 30 - 3a = 14.
Step 8: Combine like terms: -2a + 30 = 14.
Step 9: Move 30 to the other side: -2a = 14 - 30.
Step 10: Simplify: -2a = -16.
Step 11: Divide by -2: a = 8.

Arithmetic Progression – Understanding the properties of arithmetic sequences, including how to derive terms based on the first term and common difference.
Algebraic Manipulation – Solving linear equations to find unknown variables.