Question

Which term of the A.P. 10, 8, 6, … is $ - 28$?

Answer 1

Hint: Firstly, know about the A.P that is arithmetic progression which means that the sequence of numbers with a common difference between any two consecutive numbers. Use the formula of Arithmetic progression sequence for the $n^{th}$ terms that is \[{a_n} = a + \left( {n - 1} \right)d\] where, a is the initial term of the A.P. series and d is the common difference of successive numbers. Calculate the value of n.

Complete step-by-step answer:
The given A.P. series is 10, 8, 6, … and the nth terms is $ - 28$.
Now, we know about the formula of Arithmetic progression sequence for the $n^{th}$ terms that is \[{a_n} = a + \left( {n - 1} \right)d\].
Now, calculate the value of $n$. Substitute the value of $a = 10,d = - 2\left( {8 - 10} \right),$ and ${a_n} = - 28$ in the expression \[{a_n} = a + \left( {n - 1} \right)d\].
\[ \Rightarrow - 28 = 10 + \left( {n - 1} \right)\left( { - 2} \right)\]
Now, we simplify the above equation and get the value of n:
\[ \Rightarrow - 28 = 10 - 2n + 2\]
\[ \Rightarrow - 2n = - 28 - 10 - 2\]
\[ \Rightarrow - 2n = - 40\]
\[ \Rightarrow 2n = 40\]
On the further simplification, the following is obtained:
\[ \Rightarrow n = \dfrac{{40}}{2}\]
\[ \Rightarrow n = 20\]

\[\therefore \] The value of n is 20.

Note: The general formula of the Arithmetic progression is \[a,a + d,a + 2d,a + 3d,...\], where a is the initial term of the AP and d is the common difference of successive numbers. The definition of the arithmetic progression (A.P.) is the sequence of numbers with a common difference between any two consecutive numbers. For example: \[1,2,3,4,...\] and \[1,3,5,7,...\] both are arithmetic progression because of the difference of any two consecutive numbers.