Question

In the following questions, two statements (i) and (ii) are given. Choose the valid statement.

1. In an A.P., T₁₂ = 37, d = 3 then a = 4.
2. If 1 + 6 + 11 + ... + x = 189 then x = 41.

विकल्प

• Only (i)

• Only (ii)

• Both (i) and (ii)

• Neither (i) nor (ii)

Answer 1

Both (i) and (ii)

Explanation:

(i) Given:

T₁₂ = 37, d = 3, n = 12

T₁₂ = a + (n − 1)d

37 = a + (12 − 1)3

37 = a + (11)3

37 = a + 33

37 − 33 = a

a = 4

(ii) a = 1, d = 5 S_n = 189

`S_n = n/2[2a + (n - 1)d]`

189 = `n/2[2(1) + (n - 1)5]`

189 × 2 = n[2 + 5n − 5]

378 = n[5n − 3]

5n² − 3n − 378 = 0

Using the discriminant method:

n = `(3 ± sqrt((-3)^2 - 4(5)(-378)))/10`

= `(3 ± sqrt(9 + 7560))/10`

= `(3 ± 87)/10`

= `90/10`

= 9

x = T₉

⇒ T₉ = a + (9 − 1)d

x = 1 + 8(5)

x = 1 + 40

x = 41