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If the 2nd term of an arithmetic progression is 8 and the 5th term is 14, what i
If the 2nd term of an arithmetic progression is 8 and the 5th term is 14, what is the 3rd term?
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Q1
If the 2nd term of an arithmetic progression is 8 and the 5th term is 14, what is the 3rd term?
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Let the first term be a and the common difference be d. From the equations a + d = 8 and a + 4d = 14, we can find the 3rd term a + 2d = 10.
Questions & Step-by-step Solutions
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Q: If the 2nd term of an arithmetic progression is 8 and the 5th term is 14, what is the 3rd term?
Solution:
Let the first term be a and the common difference be d. From the equations a + d = 8 and a + 4d = 14, we can find the 3rd term a + 2d = 10.
Steps: 10
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Step 1: Identify the first term of the arithmetic progression as 'a' and the common difference as 'd'.
Step 2: Write the equation for the 2nd term: a + d = 8.
Step 3: Write the equation for the 5th term: a + 4d = 14.
Step 4: Now, we have two equations: a + d = 8 and a + 4d = 14.
Step 5: From the first equation (a + d = 8), we can express 'a' in terms of 'd': a = 8 - d.
Step 6: Substitute 'a' in the second equation (a + 4d = 14): (8 - d) + 4d = 14.
Step 7: Simplify the equation: 8 + 3d = 14.
Step 8: Solve for 'd': 3d = 14 - 8, so 3d = 6, which gives d = 2.
Step 9: Now, substitute 'd' back into the equation for 'a': a = 8 - d = 8 - 2 = 6.
Step 10: Now we can find the 3rd term: 3rd term = a + 2d = 6 + 2*2 = 6 + 4 = 10.
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