If the 2nd term of an arithmetic progression is 10 and the 5th term is 16, what

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Question: If the 2nd term of an arithmetic progression is 10 and the 5th term is 16, what is the 3rd term?

Options:

Correct Answer: 12

Solution:

Let the first term be a and the common difference be d. From a + d = 10 and a + 4d = 16, we can find a + 2d = 12, which is the 3rd term.

If the 2nd term of an arithmetic progression is 10 and the 5th term is 16, what is the 3rd term?

If the 2nd term of an arithmetic progression is 10 and the 5th term is 16, what is the 3rd term?

Step 1: Identify the terms of the arithmetic progression. The 2nd term is given as 10 and the 5th term is given as 16.
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 = 10.
Step 4: Write the equation for the 5th term: a + 4d = 16.
Step 5: Now, we have two equations: a + d = 10 and a + 4d = 16.
Step 6: To find 'd', subtract the first equation from the second: (a + 4d) - (a + d) = 16 - 10.
Step 7: This simplifies to 3d = 6, so d = 2.
Step 8: Now, substitute d back into the first equation: a + 2 = 10.
Step 9: Solve for 'a': a = 10 - 2, so a = 8.
Step 10: Now, find the 3rd term using the formula: 3rd term = a + 2d.
Step 11: Substitute the values of 'a' and 'd': 3rd term = 8 + 2*2.
Step 12: Calculate: 3rd term = 8 + 4 = 12.

Arithmetic Progression (AP) – An arithmetic progression is a sequence of numbers in which the difference between consecutive terms is constant.
Finding Terms in AP – To find specific terms in an AP, use the formula for the nth term: T_n = a + (n-1)d.
System of Equations – The problem involves solving a system of equations to find the first term and common difference.