Question 36 of 44intermediate🔧 ApplyShort Answer3 marks

The first term of an AP is 5, the last term is 45 and the sum is 400. Find the number of terms and the common difference.

Correct Answer

Number of terms = 16, Common difference = 8/3

Exercise: EXERCISE 5.3 | Q: 5 | (Chapter: Page 21)
For More Understanding

Explanation

This question tests the application of sum formula and nth term formula of an AP. Students need to first find n using the sum formula S = n/2(a + l), then use the nth term formula l = a + (n-1)d to find the common difference.

Solution Steps

  1. Step 1: Given: First term (a) = 5, Last term (l) = 45, Sum (S) = 400

  2. Step 2: Using sum formula: S = n/2 × (a + l)

  3. Step 3: Substituting values: 400 = n/2 × (5 + 45)

  4. Step 4: Simplifying: 400 = n/2×502 \times 50 = 25n

  5. Step 5: Therefore, n = 400/25 = 16 terms

  6. Step 6: Using nth term formula: l = a + (n-1)d

  7. Step 7: Substituting: 45 = 5 + (16-1)d

  8. Step 8: Simplifying: 45 = 5 + 15d

  9. Step 9: Therefore, 40 = 15d, so d = 40/15 = 8/3

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