In an arithmetic progression, if the 4th term is 20 and the 7th term is 26, what

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Question: In an arithmetic progression, if the 4th term is 20 and the 7th term is 26, what is the first term?

Options:

Correct Answer: 12

Solution:

Let the first term be a and the common difference be d. From the equations a + 3d = 20 and a + 6d = 26, we can solve for a and find it to be 12.

In an arithmetic progression, if the 4th term is 20 and the 7th term is 26, what is the first term?

In an arithmetic progression, if the 4th term is 20 and the 7th term is 26, what is the first term?

Step 1: Understand that in an arithmetic progression (AP), each term is found by adding a common difference (d) to the previous term.
Step 2: Let the first term be 'a'. The 4th term can be expressed as 'a + 3d'.
Step 3: According to the question, the 4th term is 20. So, we can write the equation: a + 3d = 20.
Step 4: The 7th term can be expressed as 'a + 6d'.
Step 5: According to the question, the 7th term is 26. So, we can write the equation: a + 6d = 26.
Step 6: Now, we have two equations: a + 3d = 20 and a + 6d = 26.
Step 7: To find 'd', subtract the first equation from the second: (a + 6d) - (a + 3d) = 26 - 20.
Step 8: This simplifies to 3d = 6, so d = 2.
Step 9: Now that we have 'd', substitute it back into the first equation: a + 3(2) = 20.
Step 10: This simplifies to a + 6 = 20, so a = 20 - 6.
Step 11: Therefore, a = 14.

Arithmetic Progression – Understanding the formula for the nth term of an arithmetic progression, which is given by a + (n-1)d, where a is the first term and d is the common difference.
System of Equations – Solving simultaneous equations to find unknown variables, in this case, the first term and common difference.