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Chapter 5 · Question 3

How many terms are there in the AP 7,10,13,…,437,10,13,\ldots,43?

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Q3

How many terms are there in the AP 7,10,13,…,437,10,13,\ldots,43?

Answer Revealed
Direct Answer:
Here a=7a=7, d=3d=3, and an=43a_n=43. Using an=a+(n−1)da_n=a+(n-1)d, 43=7+(n−1)343=7+(n-1)3, so 36=3(n−1)36=3(n-1), n=13n=13.

Simple Explanation

Put the last term in the nth-term formula. There are 1313 terms.

Exam-Ready Structure

For the AP, a=7a=7, d=3d=3, and final term l=43l=43. Use l=a+(n−1)dl=a+(n-1)d: 43=7+3(n−1)43=7+3(n-1). Hence 36=3(n−1)36=3(n-1), so n−1=12n-1=12 and n=13n=13.

Key Points

  • Here a=7a=7, d=3d=3, and an=43a_n=43.
  • Use the NCERT formula or theorem carefully.
  • Write units and final conclusion where applicable.

Related Questions

Q4

State the formula for the sum of first nn terms of an AP. Find the sum of first 20 natural numbers.

Q5

Reena starts with a monthly salary of ₹8000 and gets an annual increment of ₹500. What will be her salary in the 10th year?

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