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

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

Options:

Correct Answer: 10

Solution:

Let the first term be a and the common difference be d. From the given terms, we have a + 4d = 20 and a + 9d = 35. Solving these gives a = 10.

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.

Arithmetic Progression – An arithmetic progression (AP) is a sequence of numbers in which the difference between consecutive terms is constant.
Term Calculation – Understanding how to calculate specific terms in an AP using the first term and common difference.
Simultaneous Equations – The ability to set up and solve simultaneous equations derived from the terms of the AP.