Find the required term of the following sequence using sequence formul

1.	Find the required term of the following sequence using sequence formula:(i) 2, 10, 50, … (6th term)(ii) 100, 50, 25, … (7th term)
Answer» (i) 2, 10, 50, … (6th term) Here. a = 2, r = 10/2 = 5, n = 6 T₆ = a.r^n-1 ∴ T₆ = 2.(5)^6-1 = 2 (5)⁵ = 2 × 3125 = 6250 (ii) 100, 50, 25, … (7th term) Here, a = 100; r = 50/100 = 1/2 = n = 7 T_n = a.r^n-1 ∴T₇ = \(100(\frac{1}{2})^7−1\) = \(100(\frac{1}{2})^6\) = 100/64 = 25/16

Find the required term of the following sequence using sequence formula:(i) 2, 10, 50, … (6th term)(ii) 100, 50, 25, … (7th term)

Answer»

(i) 2, 10, 50, … (6th term)

Here. a = 2, r = 10/2 = 5, n = 6

T₆ = a.r^n-1

∴ T₆ = 2.(5)^6-1

= 2 (5)⁵

= 2 × 3125

= 6250

(ii) 100, 50, 25, … (7th term)

Here, a = 100; r = 50/100 = 1/2 = n = 7

T_n = a.r^n-1

∴T₇ = \(100(\frac{1}{2})^7−1\)

= \(100(\frac{1}{2})^6\)

= 100/64 = 25/16