Question 38 of 51intermediate🔧 ApplyShort Answer3 marks

Determine the AP whose third term is 16 and whose 7th7^{th} term exceeds the 5th5^{th} term by 12.

Correct Answer

4, 10, 16, 22, 28, ...

Exercise: END-OF-CHAPTER EXERCISES | Q: 2 | (Page 21)
For More Understanding

Explanation

The problem requires finding the first term 'a' and common difference 'd' of an AP using the given conditions. The formula for the nth term of an AP, t_n = a + (n-1)d, is applied to the 3rd, 5th, and 7th terms to form equations. Solving these equations yields the values of a and d, which are then used to write the complete AP.

Solution Steps

  1. Step 1: Let the first term of the AP be 'a' and the common difference be 'd'. The nth term is given by t_n = a + (n-1)d.

  2. Step 2: Given the 3rd term is 16, so a + 2d = 16.

  3. Step 3: Given the 7th term exceeds the 5th term by 12, so (a + 6d) - (a + 4d) = 12. Simplifying this gives 2d = 12, so d = 6.

  4. Step 4: Substitute d = 6 into a + 2d = 16 to get a + 12 = 16, which gives a = 4.

  5. Step 5: Using a = 4 and d = 6, the required AP is 4, 10, 16, 22, 28, ...

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