NCERT Class X Chapter 5: Arithmetic Progression Exercise 5.1 Question 4 (v)
NCERT Class X Chapter 5: Arithmetic Progression Exercise 5.1 Question 4 (v)
Question:
Which of the following are APs ? If they form an AP, find the common difference d and write three more terms. 3, 3+√2, 3+2√2, 3+3√2,...
Given:
The sequence is 3, 3+√2, 3+2√2, 3+3√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 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}. Then a1 = 3, a2 = 3+√2, a3 = 3+2√2, a4 = 3+3√2, ...
We find the difference between consecutive terms:
a2 - a1 = (3+√2) - 3 = 3 + √2 - 3 = √2
a3 - a2 = (3+2√2) - (3+√2) = 3 + 2√2 -3 -√2 = √2
a4 - a3 = (3+3√2) - (3+2√2) = 3 + 3√2 - 3 - 2√2 = √2
Since the difference between consecutive terms is constant and equal to √2, the given sequence is an AP with common difference d = √2.
The next three terms are:
a5 = a4 + d = 3 + 3√2 + √2 = 3 + 4√2
a6 = a5 + d = 3 + 4√2 + √2 = 3 + 5√2
a7 = a6 + d = 3 + 5√2 + √2 = 3 + 6√2
Result:
The given sequence is an AP with common difference d = √2. The next three terms are 3+4√2, 3+5√2, and 3+6√2.
Next question solution:
NCERT Class X Chapter 5: Arithmetic Progression Exercise 5.1 Question 4 (vi).
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