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Arithmetic Progressions
EXERCISE 5.1
CBSE_NCERT_TEXTBOOK
Grade 10

Question:

For the following APs, write the first term and the common difference: (i) 3, 1, – 1, – 3, . . . (ii) – 5, – 1, 3, 7, . . . (iii) 1 5 9 13 , , , , 3 3 3 3 . . . (iv) 0.6, 1.7, 2.8, 3.9, . . .

Step-by-Step Solution

Key Concept: In an arithmetic progression (AP) the first term $a$ is the first listed number. The common difference $d$ is obtained by subtracting any term from the next term, i.e., $d = t_{n+1} - t_n$. Once $a$ and $d$ are known, the AP is completely determined.
1. Identify the first term
The first term $a$ is simply the first number of the given sequence.

2. Find the common difference
Compute $d = \text{second term} - \text{first term}$. (The same value will be obtained for any consecutive pair if the sequence is truly an AP.)

(i) 3, 1, –1, –3, …
- First term: $a = 3$
- Common difference: $d = 1 - 3 = -2$

(ii) –5, –1, 3, 7, …
- First term: $a = -5$
- Common difference: $d = (-1) - (-5) = 4$

(iii) 1, 5, 9, 13, …
- First term: $a = 1$
- Common difference: $d = 5 - 1 = 4$

(iv) 0.6, 1.7, 2.8, 3.9, …
- First term: $a = 0.6$
- Common difference: $d = 1.7 - 0.6 = 1.1$

Thus for each AP we have identified $a$ and $d$ as required.

Correct Answer: (i) $a = 3$, $d = -2$; (ii) $a = -5$, $d = 4$; (iii) $a = 1$, $d = 4$; (iv) $a = 0.6$, $d = 1.1$
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