Question 42 of 44intermediate🔧 ApplyShort Answer3 marks

An AP consists of 50 terms of which 3rd term is 12 and the last term is 106. Find the 29th term.

Correct Answer

The 29th term of the AP is 64.

Exercise: EXERCISE 5.2 | Q: 8 | (Chapter: Page 14)
For More Understanding

Explanation

This question tests the application of the nth term formula of an AP. Students need to set up two equations using the given information about the 3rd term and the last (50th) term, solve for the first term 'a' and common difference 'd', and then use these values to find the 29th term.

Solution Steps

  1. Step 1: Write the formula for the nth term of an AP: aₙ = a + (n-1)d

  2. Step 2: Using the given information, form two equations:

    • For 3rd term: a + 2d = 12 ... (i)
    • For last term (50th): a + 49d = 106 ... (ii)

  3. Step 3: Subtract equation (i) from equation (ii): (a + 49d) - (a + 2d) = 106 - 12 47d = 94 d = 2

  4. Step 4: Substitute d = 2 in equation (i): a + 2(2) = 12 a + 4 = 12 a = 8

  5. Step 5: Find the 29th term using the formula: a₂₉ = a + 28d a₂₉ = 8 + 28(2) a₂₉ = 8 + 56 a₂₉ = 64

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