Question

Find the middle term of A.P. 6, 13, 20, ......., 230.

Answer 1

Identify the first term and common difference:

a = 6

d = 13 − 6 = 7

Given, t_n = 230

Find the number of terms (n):

Use the n^th-term formula:

t_n = a + (n − 1)d

230 = 6 + (n – 1)(7)

230 – 6 = 7(n – 1)

224 = 7(n – 1)

n – 1 = `224/7`

n – 1 = 32

n = 32 + 1

n = 33

Find the middle term:

Since there are 33 terms (odd number), the middle term is the:

`(n + 1)/2`

= `(33 + 1)/2`

= `34/2`

= 17^th term

Now find the 17^th term:

t₁₇ = 6 + (17 − 1)(7)

t₁₇ = 6 + 16(7)

t₁₇ = 6 + 112

t₁₇ = 118