If the 2nd term of an arithmetic progression is 8 and the 4th term is 14, what i

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Question: If the 2nd term of an arithmetic progression is 8 and the 4th term is 14, what is the 1st term?

Options:

Correct Answer: 6

Solution:

Let the first term be a and the common difference be d. From the equations a + d = 8 and a + 3d = 14, we can find a = 6.

If the 2nd term of an arithmetic progression is 8 and the 4th term is 14, what is the 1st term?

If the 2nd term of an arithmetic progression is 8 and the 4th term is 14, what is the 1st 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 4th term: a + 3d = 14.
Step 5: Now you have two equations: a + d = 8 and a + 3d = 14.
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 + 3d = 14): a + 3(8 - a) = 14.
Step 8: Simplify the equation: a + 24 - 3a = 14.
Step 9: Combine like terms: -2a + 24 = 14.
Step 10: Solve for 'a': -2a = 14 - 24, which simplifies to -2a = -10.
Step 11: Divide both sides by -2: a = 5.

Arithmetic Progression (AP) – An arithmetic progression is a sequence of numbers in which the difference between consecutive terms is constant.
Terms of an AP – The nth term of an arithmetic progression can be expressed as a + (n-1)d, where a is the first term and d is the common difference.
Solving Linear Equations – The problem involves setting up and solving linear equations based on the given terms of the arithmetic progression.