Question

Please please help me out

Answer 1

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:

Step(i):-

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

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

Step(ii):-

put n=1

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

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

Final 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