NCERT Exemplar Solutions
Class 10 - Mathematics - CHAPTER 5: Arithematic Progressions - Exercise 5.3Question 10
Class 10 - Mathematics - CHAPTER 5: Arithematic Progressions - Exercise 5.3
Question. 10
Is 55 a term of AP \(7,10,13,\ldots\)? If yes, which term?
Answer:
Yes, the 17th term.
Detailed Answer with Explanation:
Step 1: Recall the formula for the \(n\)th term of an AP:
\(a_n = a + (n-1) \times d\)
where \(a\) = first term, \(d\) = common difference, and \(n\) = term number.
Step 2: Identify values from the given AP \(7, 10, 13, \ldots\):
- First term \(a = 7\)
- Common difference \(d = 10 - 7 = 3\)
- We need to check if 55 is a term.
Step 3: Put values in the formula:
\(55 = 7 + (n-1) \times 3\)
Step 4: Simplify the equation:
\(55 - 7 = (n-1) \times 3\)
\(48 = (n-1) \times 3\)
Step 5: Solve for \(n-1\):
\(n-1 = 48 \div 3 = 16\)
Step 6: Find \(n\):
\(n = 16 + 1 = 17\)
Final Answer: 55 is the 17th term of the AP.