Find the 19th term of the AP (1.2, 2.7, 4.2, ...).
Answer and explanation
Correct answer: 28.2
The nth-term formula is a_n = a + (n − 1)d. The first term is a = 1.2, and the common difference is d = 2.7 − 1.2 = 1.5; the next difference 4.2 − 2.7 also confirms this. For n = 19, a_19 = 1.2 + (19 − 1) × 1.5 = 1.2 + 18 × 1.5. Since 18 × 1.5 = 27, the result is 28.2. Therefore option D is correct. A common error is to use 19 differences rather than 18, which would produce 29.7, or to add the decimal difference incorrectly. The first term corresponds to zero added differences, so the 19th term necessarily uses 18 increments of 1.5.
Frequently asked questions
What is the correct answer to this question?
28.2
Why is this the correct answer?
The nth-term formula is a_n = a + (n − 1)d. The first term is a = 1.2, and the common difference is d = 2.7 − 1.2 = 1.5; the next difference 4.2 − 2.7 also confirms this. For n = 19, a_19 = 1.2 + (19 − 1) × 1.5 = 1.2 + 18 × 1.5. Since 18 × 1.5 = 27, the result is 28.2. Therefore option D is correct. A common error is to use 19 differences rather than 18, which would produce 29.7, or to add the decimal difference incorrectly. The first term corresponds to zero added differences, so the 19th term necessarily uses 18 increments of 1.5.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Arithmetic Progressions (AP). Topic: Finding the $n$th term of an AP.
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