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Arithmetic Progressions
EXERCISE 5.2
CBSE_NCERT_TEXTBOOK
Grade 10
Question:
Which term of the AP : 3, 8, 13, 18, . . . ,is 78?
Step-by-Step Solution
Key Concept: Use the nth term formula of an arithmetic progression: \(a_n = a + (n-1)d\), where \(a\) is the first term and \(d\) is the common difference.
1. Identify the first term and common difference of the given AP. - First term \(a = 3\). - Common difference \(d = 8-3 = 5\). 2. Write the nth term formula for the AP: $$a_n = a + (n-1)d$$ 3. Substitute \(a = 3\), \(d = 5\) and \(a_n = 78\) into the formula: $$78 = 3 + (n-1)\times 5$$ 4. Solve for \(n\): \[78 - 3 = (n-1)\times 5\] \[75 = 5(n-1)\] \[n-1 = \frac{75}{5} = 15\] \[n = 15 + 1 = 16\] 5. Hence, the number 78 occurs at the 16th position in the given AP.
Correct Answer:16
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