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Anika [276]
3 years ago
13

Please please help me out

Mathematics
1 answer:
klemol [59]3 years ago
3 0

Answer:

a) t_{1}  = 12

b) The explicit formula

t_{n} = ar^{n-1} = 12(2.5)^{n-1}

c) t₁₈  = 69,849,193.096

Step-by-step explanation:

<u><em> Step(i):-</em></u>

Given that the geometric sequence

          r = 2.5

Given the fourth term of the  geometric sequence

      t_{4} = ar^{3} = 187.5

⇒ ar³ = 187.5

⇒ a (2.5)³ = 187.5

    a = \frac{187.5}{(2.5)^{3} } = 12

The explicit formula

t_{n} = ar^{n-1} = 12(2.5)^{n-1}

<u><em>Step(ii):-</em></u>

<u><em>put n=1</em></u>

t_{1} = ar^{1-1} = 12(2.5)^{1-1}  = 12 (2.5)^{0} = 12

The 18^{th} of the geometric sequence

t_{18} = ar^{18-1} = a r^{17}

t_{18} = 12( 2.5)^{17}

t₁₈  = 69,849,193.096

<u><em>Final answer:-</em></u>

a) t_{1}  = 12

b) The explicit formula

t_{n} = ar^{n-1} = 12(2.5)^{n-1}

c) t₁₈  = 69,849,193.096

<em></em>

<em></em>

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