Question 21 of 44intermediate🔧 ApplyShort Answer3 marks

Find the 20th term from the last term of the AP: 3, 8, 13, . . ., 253.

Correct Answer

The 20th term from the last term of the given AP is 158.

Exercise: EXERCISE 5.2 | Q: 17 | (Page Page 15)
For More Understanding

Explanation

This question tests the student's understanding of finding a specific term from the end of an AP. The approach involves first determining the total number of terms in the AP using the last term formula, and then calculating the position of the required term from the beginning. The 20th term from the last is the (n - 20 + 1)th term from the beginning, where n is the total number of terms.

Solution Steps

  1. Step 1: Identify the given values: First term (a) = 3, Common difference (d) = 8 - 3 = 5, Last term (l) = 253

  2. Step 2: Find the total number of terms (n) using the formula: a_n = a + (n - 1)d

  3. Substituting values: 253 = 3 + (n - 1) × 5

  4. 253 = 3 + 5n - 5

  5. 253 = 5n - 2

  6. 255 = 5n

  7. n = 51

  8. Step 3: The 20th term from the last term is the (51 - 20 + 1)th = 32nd term from the beginning.

  9. Step 4: Calculate the 32nd term using: a_32 = a + (32 - 1)d = 3 + 31×531 \times 5 = 3 + 155 = 158

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