Question

which term of the AP 3 8 13 18 is 78​

Answer 1

Given,

The terms of the arithmetic progration are 3,8,13,18,.......

Here, the first term (a) = 3

The common difference (d) = a2-a1

d = 8-3

d = 5

The n th term is 78.

a(n) = 78

To find out,

Which term of the AP is 78.

Solution:

$a(n) = a + (n - 1)d \\ \\ 78 \: \: \: = 3 + (n - 1)5 \\ \\ 78 \: \: \: = 3 + 5n - 5 \\ \\ 78 \: \: \: = - 2 + 5n \\ \\ 78 + 2 = 5n \\ \\ 80 \: \: \: = 5n \\ \\ n \: = \frac{80}{5} \\ \\ n \: \: \: = 16$

Therefore 78 is 16th term of the AP.

Answer 2

Let a(n) be the required term of the AP: 3, 8, 13, 18,...

Here, a = 3, d = 8 – 3 = 5 and an = 78

Now, an = a + (n – 1)d

⇒ 78 = 3 + (n – 1) × 5 ⇒ 78 – 3 = (n – 1) × 5

⇒ 75 = (n – 1) × 5

⇒ 75/5 = n – 1 ⇒ 15 = n – 1 ⇒ n = 15 + 1 = 16

Hence, 16th term of given AP is 78.