For the AP : 3 , 1 , – 1 , – 3 , . . ., write the first term a and the common difference d.
Step-by-Step Solution
Key Concept: In an arithmetic progression (AP) the first term is denoted by $a$ and the common difference $d$ is the constant difference between any two successive terms, i.e., $d = T_{n+1} - T_n$.
1. Identify the first term of the given AP.
The sequence starts as $3, 1, -1, -3, \dots$; therefore the first term $a = 3$.
2. Find the common difference $d$ using any two consecutive terms.
Using the first two terms: \[d = 1 - 3 = -2.\]
(Verification with other consecutive terms: $-1 - 1 = -2$, $-3 - (-1) = -2$, confirming the constant difference.)
3. Hence, the required values are: \[a = 3, \quad d = -2.\]
Correct Answer: a = 3, d = -2