Fill in the blanks In the following table, given that ‘a’ is the f

1.	Fill in the blanks In the following table, given that ‘a’ is the first term, ‘d’ is the common difference and an the nth term of the A.P.
Answer» (i) a = 7, d = 3, n = 8, a_n =? a_n = a + (n – 1)d a₈= 7 + (8 – 1)3 = 7 + 7 × 3 = 7 + 21 ∴ a₈ = 28 (ii) a = -18, d =?, n = 10, a_n = 0 a_n = a + (n – 1)d 0 = -18 + (10 – 1)d 0 = -18 + 9d 18 = 9d 9d = 18 ∴ d = \(\frac{18}{9}\) = 2 (iii) a =?, d = -3, n = 18, a_n = -5 a_n = a + (n – 1)d -5 = a + (18 – 1) (-3) = a + 17(-3) -6 = 1 – 51 ∴ a = -5 + 51 = 46 (iv) a = -18.9, d = 2.5, n =? a_n = 3.6 a_n = a + (n – 1) d 3.6 = -18.9 + (n – 1) (2.5) 3.6 = -18.9 + 2.5n – 2.5 3.6 = 2.5n – 21.4 2.5n = 3.6 + 21.4 2.5n = 25 n = \(\frac{25}{2.5}\) = \(\frac{250}{25}\) ∴ n = 10. (v) a = 3.5, d = 0, n = 105, a_n =? a_n = a + (n – 1) d = 3.5 + (105 – 1) (0) = 3.5+ 104 × 0 = 3.5 +0 ∴ a_n = 3.5

Fill in the blanks In the following table, given that ‘a’ is the first term, ‘d’ is the common difference and an the nth term of the A.P.

Answer»

(i) a = 7, d = 3, n = 8, a_n =?

a_n = a + (n – 1)d

a₈= 7 + (8 – 1)3

= 7 + 7 × 3 = 7 + 21

∴ a₈ = 28

(ii) a = -18, d =?, n = 10, a_n = 0

a_n = a + (n – 1)d

0 = -18 + (10 – 1)d

0 = -18 + 9d 18 = 9d

9d = 18

∴ d = \(\frac{18}{9}\) = 2

(iii) a =?, d = -3, n = 18, a_n = -5

a_n = a + (n – 1)d

-5 = a + (18 – 1) (-3)

= a + 17(-3)

-6 = 1 – 51

∴ a = -5 + 51 = 46

(iv) a = -18.9, d = 2.5, n =? a_n = 3.6

a_n = a + (n – 1) d

3.6 = -18.9 + (n – 1) (2.5)

3.6 = -18.9 + 2.5n – 2.5

3.6 = 2.5n – 21.4

2.5n = 3.6 + 21.4

2.5n = 25

n = \(\frac{25}{2.5}\) = \(\frac{250}{25}\)

∴ n = 10.

(v) a = 3.5, d = 0, n = 105, a_n =?

a_n = a + (n – 1) d

= 3.5 + (105 – 1) (0)

= 3.5+ 104 × 0

= 3.5 +0

∴ a_n = 3.5