Question

The first term of an AP is 5 and the common difference is -3 .Find the 11th term of the AP.

Answer 1

In this particular type of question we have to use the general formula of an AP which is ${a_n} = a + \left( {n - 1} \right)d$ to get the desired result. As they have given first term and the common difference.

Complete step-by-step answer:
First term (a) = 5
Common difference(d) = -3
n=11
11th term = ${a_{11}}$
$\begin{gathered}
  {a_n} = a + \left( {n - 1} \right)d \\
   \Rightarrow {a_{11}} = 5 + \left( {11 - 1} \right)\left( { - 3} \right) \\
   \Rightarrow {a_{11}} = 5 - 30 = - 25 \\
\end{gathered} $
Thus the 11th term is -25.

Note- Remember to recall the basic formula of AP while solving such questions. Note that if the common difference between consecutive terms is positive, we say that the sequence is increasing. On the other hand, when the difference is negative we say that the sequence is decreasing. The above AP is thus decreasing.