Question

Find the 18 th term of the ap -50,-35,-20,-5

Answer 1

Answer:

we know that,

n-th term = a+ (n-1)d

where a= first term, d= common difference

Here, n= 18 , a= -50, d= -35-(-50)=15

Therefore, 18th term = -50+ (18-1)×15

= -50 + 17×15

= -50 + 255

=205

Answer 2

Given AP: -50, -35, -20, -5 . . . . .

We have to find the 18th term. We know that any term of an AP can be expressed of the form;

a$_{\sf n}$ = a + (n - 1)d

(Where an is the position of the term)

So the 18th term will be a₁₈ = a + (n - 1)d

But we have to find the first term and the common difference first.

The first term (a) of the given arithmetic progression is -50.

The common difference (d) can be found out by subtracting a succeeding term by the preceding term.

Common difference (d) = a₂ - a₁

Common difference (d) = -35 - (-50)

Common difference (d) = -35 + 50

Common difference (d) = 15

Now that we know the first term and common difference, we can find the 18th term of the AP.

⇔ a$_{\sf n}$ = a + (n - 1)d

a = -50; d = 15; n = 18.

⇔ a₁₈ = -50 + (18 - 1)15

⇔ a₁₈ = -50 + (17)15

⇔ a₁₈ = -50 + 255

⇔ a₁₈ = 205

∴ The 18th term of the given AP is 205.