Question

2. Find the 10th term and common ratio of the geometric sequence

Answer 1

GEOMETRIC PROGRESSION :
A sequence a1, a2, a3 ………….. an Is called a geometric sequence if a(n+1) = anr, where r is a non zero constant. Here, a1 is the first term and the constant r is called common ratio. The sequence is also called a geometric progression(G.P)
a1 = a , r = a(ⁿ+1)/ aⁿ
General term of a geometric sequence is
tn = arⁿ-1
General form of G.P is a, a r , a r ²,.........

SOLUTION :
GIVEN : a = ¼, n = 10
Common ratio r = a(ⁿ+1)/ aⁿ
r= (-1/2)/(1/4) = (-1/2) x (4/1) = -2
r = -2

General term of a geometric sequence is
tn = arⁿ-1

t₁₀ = (1/4) (-2)^(10-1)
t₁₀ = (1/4) (-2)^9
t₁₀ = (1/4) (-512)
t₁₀ = - 512/4
t₁₀ = -128 or -2^7

Hence, the 10th term is -128 or -2^7 & common ratio is -2

HOPE THIS WILL HELP YOU…

Answer 2

Solution :

Given series 1/4 , -1/2 , 1 , -2 ,...

a2/a1 = (-1/2)/(1/4) = -2

a3/a2 = 1/(-1/2) = -2

Since , a2/a1 = a3/a2

So, Given series is in G.P .

common ratio ( r ) = -2 ,

nth term = an = a × r^n-1

here , n = 10 ,

a10 = ( 1/4 ) × ( -2 )^10-1

= ( 1/4 ) × (-2^9)

= -2^9/2²

= -2^7

= -128

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