Question

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

Answer 1

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.