Question

Find the 20th term of the Arithmetic Progression (A.P.) 10, 7, 4, …

• A. -47
• B. 47
• C. -57
• D. 67

Hint:

In an A.P., if the common difference is negative, terms will decrease successively. Use \( a_n = a + (n-1)d \) to find any term.

Answer 1

The Correct Option is A

Step 1: Identify the first term and common difference.
First term, \( a = 10 \)
Common difference, \( d = 7 - 10 = -3 \)

Step 2: Recall the nth term formula.
\[ a_n = a + (n - 1)d \]
Step 3: Substitute the given values.
\[ a_{20} = 10 + (20 - 1)(-3) \] \[ a_{20} = 10 + 19(-3) = 10 - 57 = -47 \]
Step 4: Conclusion.
Hence, the 20th term of the A.P. is \( \boxed{-47} \).