In an arithmetic progression, if the 5th term is 20 and the 10th term is 35, wha

In an arithmetic progression, if the 5th term is 20 and the 10th term is 35, what is the first term?

In an arithmetic progression, if the 5th term is 20 and the 10th term is 35, 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 5th term can be expressed as 'a + 4d'.
Step 3: According to the question, the 5th term is 20. So, we can write the equation: a + 4d = 20.
Step 4: The 10th term can be expressed as 'a + 9d'.
Step 5: According to the question, the 10th term is 35. So, we can write the equation: a + 9d = 35.
Step 6: Now, we have two equations: a + 4d = 20 and a + 9d = 35.
Step 7: To find 'd', subtract the first equation from the second: (a + 9d) - (a + 4d) = 35 - 20.
Step 8: This simplifies to 5d = 15, so d = 3.
Step 9: Now, substitute d back into the first equation: a + 4(3) = 20.
Step 10: This simplifies to a + 12 = 20, so a = 20 - 12.
Step 11: Therefore, a = 8. The first term is 8.

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