NCERT Class X Chapter 5: Arithmetic Progression Exercise 5.1 Question 4 (xii)
NCERT Class X Chapter 5: Arithmetic Progression Exercise 5.1 Question 4 (xii)
Question:
Which of the following are APs ? If they form an AP, find the common difference d and write three more terms. √2, √8, √18, √32, ...
Given:
The sequence is √2, √8, √18, √32, ...
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. We have:
a1 = √2 = √(2 × 12) = √2
a2 = √8 = √(2 × 22) = 2√2
a3 = √18 = √(2 × 32) = 3√2
a4 = √32 = √(2 × 42) = 4√2
The common difference is:
d = a2 - a1 = 2√2 - √2 = √2
d = a3 - a2 = 3√2 - 2√2 = √2
d = a4 - a3 = 4√2 - 3√2 = √2
Since the common difference is constant (d = √2), the sequence is an AP.
The next three terms are:
a5 = a4 + d = 4√2 + √2 = 5√2 = √50
a6 = a5 + d = 5√2 + √2 = 6√2 = √72
a7 = a6 + d = 6√2 + √2 = 7√2 = √98
Result:
The sequence is an AP with a common difference of √2. The next three terms are √50, √72, and √98.
Next question solution:
NCERT Class X Chapter 5: Arithmetic Progression Exercise 5.1 Question 4 (xiii).
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