Question

please solve it.

a= -18.9 , d=2.5 , n=? ,an=3.6
formulla:- an=a+(n-1)d

Answer 1

answer : an = a + ( n - 1 ) .d

3.6 = - 18.9 + ( n - 1 ) 2.5

3.6 + 18.9 = 2.5n - 2.5

3.6 + 18.9 + 2.5 = 2.5n

25 = 2.5n

25/ 2.5 = n

10 = n

Answer 2

For the given values of a, d, and $a_n$, n will be 10.

Given,

a = -18.9,

d = 2.5,

$a_n=3.6$

To find,

n.

Solution,

It can be seen here that the given terms are in reference to an arithmetic progression or A. P.

An A. P. is defined as a continuous sequence of numbers in a specific order, in which the difference between any two consecutive terms or numbers is constant.

In an AP,

a = first term,

d = common difference,

$a_n=n^{th}$ term

The $n^{th}$ term is given by,

$a_n=a+(n-1)d$     ...(1)

Substituting the given values of a, d, and $a_n$ in the above equation (1),

$3.6=(-18.9)+(n-1)(2.5)$

Rearranging and simplifying,

$2.5(n-1)=3.6+18.9$

$\implies 2.5(n-1)=22.5$

$\implies n-1=\frac{22.5}{2.5}$

$\implies n=9+1$

⇒ n = 10.

Therefore, for the given values of a, d, and $a_n$, n will be 10.