If the 2nd term of an arithmetic progression is 8 and the 5th term is 20, what i

If the 2nd term of an arithmetic progression is 8 and the 5th term is 20, what is the first term?

If the 2nd term of an arithmetic progression is 8 and the 5th term is 20, what is the first term?

Step 1: Understand that in an arithmetic progression, each term is found by adding a common difference to the previous term.
Step 2: Let the first term be 'a' and the common difference be 'd'.
Step 3: Write the equation for the 2nd term: a + d = 8.
Step 4: Write the equation for the 5th term: a + 4d = 20.
Step 5: Now you have two equations: a + d = 8 and a + 4d = 20.
Step 6: From the first equation (a + d = 8), you can express 'd' in terms of 'a': d = 8 - a.
Step 7: Substitute 'd' in the second equation (a + 4d = 20) with (8 - a): a + 4(8 - a) = 20.
Step 8: Simplify the equation: a + 32 - 4a = 20.
Step 9: Combine like terms: -3a + 32 = 20.
Step 10: Move 32 to the other side: -3a = 20 - 32.
Step 11: Simplify: -3a = -12.
Step 12: Divide both sides by -3: a = 4.
Step 13: Therefore, the first term is 4.

Arithmetic Progression – An arithmetic progression (AP) is a sequence of numbers in which the difference between consecutive terms is constant.
Equations – The problem requires setting up and solving linear equations based on the properties of an arithmetic progression.