Question 37 of 51intermediate🔧 ApplyNumerical3 marks

Find the 31st31^{st} term of an AP whose 11th11^{th} term is 38 and 16th16^{th} term is 73.

Correct Answer

178

Exercise: END-OF-CHAPTER EXERCISES | Q: 1 | (Page 21)
For More Understanding

Explanation

The solution uses the nth term formula of an AP, t_n = a + (n-1)d, to set up a system of linear equations from the given 11th and 16th terms. Solving this system yields the first term 'a' and common difference 'd', which are then used to find the 31st term.

Solution Steps

  1. Step 1: Form equations using the nth term formula: a + 10d = 38 (1) and a + 15d = 73 (2).

  2. Step 2: Subtract (1) from (2) to find d: 5d = 35, so d = 7.

  3. Step 3: Substitute d = 7 into (1) to find a: a + 70 = 38, so a = -32.

  4. Step 4: Calculate the 31st term: t_31 = a + 30d = -32 + 30(7) = -32 + 210 = 178.

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