Question

Which term of the A.P.: \(20, 18, 16, \dots\) is \(-80\)?

• A. 50
• B. 51
• C. 52
• D. 53

Hint:

For A.P. problems, use the formula for the \(n\)-th term \(T_n = a + (n - 1) \times d\) to find the desired term.

Answer 1

The Correct Option is C

For an arithmetic progression (A.P.), the \(n\)-th term is given by: \[ T_n = a + (n - 1) \times d \] where \(a\) is the first term and \(d\) is the common difference. In this case, \(a = 20\) and \(d = -2\). We are given that the \(n\)-th term is \(-80\). Thus, we have: \[ -80 = 20 + (n - 1)(-2) \] \[ -80 = 20 - 2(n - 1) \] \[ -80 - 20 = -2(n - 1) \] \[ -100 = -2(n - 1) \] \[ 50 = n - 1 \] \[ n = 51 \] Thus, the correct answer is option (2).