Find the 10th term of the AP : 2,7,12,…
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Step-by-Step Solution
Step 1: Identify the first term and common difference
In an Arithmetic Progression (AP), the first term is denoted by a. From the given sequence, the first term is 2. The common difference, denoted by d, is found by subtracting any term from its succeeding term. Here, the common difference is 7−2=5.
Step 2: Identify the number of the term to find
We need to find the 10th term of the AP, so the value of n (the term number) is 10.
Step 3: Apply the formula for the nth term of an AP
The formula for the nth term of an Arithmetic Progression is an=a+(n−1)d, where an is the nth term, a is the first term, n is the term number, and d is the common difference. This formula is fundamental for finding any term in an AP. (Refer to NCERT Class 10 Mathematics - Arithmetic Progressions, Example 3, page 1).
Step 4: Substitute the values into the formula
Now we substitute the identified values of a=2, n=10, and d=5 into the formula an=a+(n−1)d to calculate the 10th term.
Step 5: Calculate the 10th term
Perform the arithmetic operations: first, subtract 1 from 10 to get 9, then multiply 9 by the common difference 5 to get 45. Finally, add this product to the first term 2 to obtain the 10th term, which is 47.