Question 22 of 51beginner🔧 ApplyNumerical2 marks

Find the 10th10^{th} and 26th26^{th} terms of the AP: 3, 8, 13, 18, ….

Correct Answer

(10th term) 48

(26th term) 128

Exercise: Exercise Set 8.2 | Q: 1 | (Page 12)
For More Understanding

Explanation

The textbook context explains that in an arithmetic progression (AP), the difference between consecutive terms is a constant value. The nth term of an AP can be written as t_n = a + (n - 1)d, where 'a' is the first term and 'd' is the common difference. By identifying these values from the given sequence and substituting them into the formula, we can calculate any specific term.

Solution Steps

  1. Step 1: Identify the first term (a) and common difference (d) from the given AP: 3, 8, 13, 18, ... Here, a = 3 and d = 8 - 3 = 5.

  2. Step 2: State the formula for the nth term of an AP: t_n = a + (n - 1)d.

  3. Step 3: Calculate the 10th term by substituting n = 10: t_10 = 3 + (10 - 1) × 5 = 3 + 9×59 \times 5 = 3 + 45 = 48.

  4. Step 4: Calculate the 26th term by substituting n = 26: t_26 = 3 + (26 - 1) × 5 = 3 + 25×525 \times 5 = 3 + 125 = 128.

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