Q. 144.0( 5 Votes )

# In a GP the 3^{rd} term is 24, and the 6^{th} term is 192. Find the 10^{th} term.

Answer :

T_{n} = ar^{n-1}

a = a, r =?, T_{n} = 24 n = 3

a = a, r =?, T_{n} = 192 n = 6

∴ 24 = a.r^{3-1}

⇒ 24 = a.r^{2}…(1)

∴ 192 = a.r^{6-1}

⇒ 192 = a.r^{5}…(2)

Divide (2) by (1) we get

⇒

⇒ r^{3} = 8

⇒ r = 2

Substituting r in 2 we get

a = 6

T_{10} = 6.2^{10-1}

= 6.2^{9}

= 3072.

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