Find the 31st term of an AP whose 11th term is 38 and the 16th term…

Question 11 of 44intermediate🔧 ApplyShort Answer3 marks

Find the 31st term of an AP whose 11th term is 38 and the 16th term is 73.

Correct Answer

The 31st term of the AP is 178.

Exercise: EXERCISE 5.2 | Q: 7 | (Page Page 14)

For More Understanding

Explanation

This question tests the understanding of the nth term formula of an Arithmetic Progression. Students need to set up two equations using the given terms, solve for the first term and common difference, and then find the required term.

Solution Steps

Step 1: We know that the nth term of an AP is given by $a_n = a + (n-1)d$ , where $a$ is the first term and $d$ is the common difference.
Step 2: Given $a_{11} = 38$ and $a_{16} = 73$ . Using the formula: $a_{11} = a + 10d = 38$ ... (1) and $a_{16} = a + 15d = 73$ ... (2)
Step 3: Subtracting equation (1) from equation (2): $(a + 15d) - (a + 10d) = 73 - 38$ , which gives $5d = 35$ , so $d = 7$ .
Step 4: Substituting $d = 7$ in equation (1): $a + 10(7) = 38$ , so $a + 70 = 38$ , therefore $a = -32$ .
Step 5: Now, finding the 31st term: $a_{31} = a + 30d = -32 + 30(7) = -32 + 210 = 178$ .

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