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

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.

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