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Verified answer
Un = a rⁿ⁻¹1) 2+4+8+16+..
a=2 , r = 4/2 = 2
un = 2 2ⁿ⁻¹ =2.2⁻¹. 2ⁿ = 2ⁿ
2) 27+9+3+...
a= 27, r = 9/27 = 1/3
un = 27. (1/3)ⁿ⁻¹ = 3³. 3¹. 3⁻ⁿ = 3⁴⁻ⁿ
3) 3 +(-6) +(12
a= 3 , r = -2
un = 3. (-2)ⁿ⁻¹ = (-3/2)(-2)ⁿ
4) 5+20+80+...
a=5 , r = 4
un = 5. 4ⁿ⁻¹ = 5/4 (4)ⁿ
5)-2 +(-4) + (-8)
a= - 2, r = 2
un = (-2)(2)ⁿ⁻¹
Un = -2/2 (2)ⁿ = - (2)ⁿ
6) 4 +(-8) +(16) +...
a = 4 , r = -2
un = 4 (-2)ⁿ⁻¹
un = 4/(-2) (-2)ⁿ = -2 (-2)ⁿ =(-2)ⁿ⁺¹
7) 3 +12+ 48 +...
a= 3, r = 4
un = 3.(4)ⁿ⁻¹
un = 3/4 (4)ⁿ
8) -5 +(-15) + (-45)
a = - 5, r = 3
un = (-5) (3)ⁿ⁻¹
un = - 5/3 (3)ⁿ
9) 8 + 2 + 1/2+...
a= 8 , r = 2/8 = 1/4
un = 8 . (1/4)ⁿ⁻¹
un = 2³. (2)⁻²ⁿ⁺²
un = (2)⁵⁻²ⁿ