NCERT Class X Chapter 5: Arithmetic Progression Example 2 (ii)
NCERT Class X Chapter 5: Arithmetic Progression Example 2(ii)
Question:
Which of the following list of numbers form an AP? If they form an AP, write the next two terms : 1, – 1, – 3, – 5, . . .
Given:
The list of numbers is 1, –1, –3, –5, . . .
To Find:
Whether the given list of numbers forms an arithmetic progression (AP). If it forms an AP, find the next two terms.
Formula:
In an arithmetic progression, the difference between consecutive terms is constant.
This constant difference is called the common difference (d).
Solution:
Let the given list of numbers be denoted by a1, a2, a3, a4, ...
Then, a1 = 1, a2 = –1, a3 = –3, a4 = –5, ...
Let's find the common difference (d):
d = a2 – a1 = –1 – 1 = –2
d = a3 – a2 = –3 – (–1) = –2
d = a4 – a3 = –5 – (–3) = –2
Since the common difference is constant (d = –2), the given list of numbers forms an arithmetic progression.
To find the next two terms, we add the common difference to the last term:
a5 = a4 + d = –5 + (–2) = –7
a6 = a5 + d = –7 + (–2) = –9
Result:
Yes, the numbers form an AP with a common difference of –2.
The next two terms are –7 and –9.
Next question solution:
NCERT Class X Chapter 5: Arithmetic Progression Example 2 (iii).
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