NCERT Class X Chapter 5: Arithmetic Progression Exercise 5.1 Question 4 (vii)
NCERT Class X Chapter 5: Arithmetic Progression Exercise 5.1 Question 4 (vii)
Question:
Which of the following are APs ? If they form an AP, find the common difference d and write three more terms. 0, – 4, – 8, –12, . . .
Given:
The sequence is 0, – 4, – 8, –12, . . .
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 arithmetic progression (AP), the difference between consecutive terms is constant. This constant difference is called the common difference (d).
Solution:
Let the given sequence be denoted by {an}, where a1 = 0, a2 = -4, a3 = -8, a4 = -12, ...
We calculate the differences between consecutive terms:
a2 - a1 = -4 - 0 = -4
a3 - a2 = -8 - (-4) = -4
a4 - a3 = -12 - (-8) = -4
Since the difference between consecutive terms is constant and equal to -4, the given sequence is an arithmetic progression (AP).
The common difference is d = -4.
To find the next three terms, we add the common difference to the last term repeatedly:
a5 = a4 + d = -12 + (-4) = -16
a6 = a5 + d = -16 + (-4) = -20
a7 = a6 + d = -20 + (-4) = -24
Result:
The given sequence is an AP with a common difference of -4. The next three terms are -16, -20, and -24.
Next question solution:
NCERT Class X Chapter 5: Arithmetic Progression Exercise 5.1 Question 4 (viii).
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