NCERT Class X Chapter 5: Arithmetic Progression Exercise 5.1 Question 4 (iii)
NCERT Class X Chapter 5: Arithmetic Progression Exercise 5.1 Question 4 (iii)
Question:
Which of the following are APs ? If they form an AP, find the common difference d and write three more terms. – 1.2, – 3.2, – 5.2, – 7.2, . . .
Given:
The sequence: – 1.2, – 3.2, – 5.2, – 7.2, . . .
To Find:
Whether the given sequence is an AP. If it is an AP, find the common difference (d) and the next three terms.
Formula:
In an AP, the common difference (d) is given by: d = an - an-1, where an and an-1 are consecutive terms.
Solution:
Let's find the difference between consecutive terms:
– 3.2 – (– 1.2) = –3.2 + 1.2 = –2
– 5.2 – (– 3.2) = –5.2 + 3.2 = –2
– 7.2 – (– 5.2) = –7.2 + 5.2 = –2
Since the difference between consecutive terms is constant and equal to –2, the given sequence is an arithmetic progression (AP).
The common difference, d = –2
To find the next three terms, we add the common difference successively:
– 7.2 + (–2) = –9.2
– 9.2 + (–2) = –11.2
– 11.2 + (–2) = –13.2
Result:
The given sequence is an AP with a common difference of –2. The next three terms are –9.2, –11.2, and –13.2.
Next question solution:
NCERT Class X Chapter 5: Arithmetic Progression Exercise 5.1 Question 4 (iv).
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