Question

Write the first five terms of the geometri.c sequence in which a1 - 8 and the common ratio is 5/2.

Answer 1

Answer:

8 , 20, 50, 125, 625/2           option D

Step-by-step explanation:

Given that,

first term a₁ = 8

common ratio (r) = $\frac{5}{2}$

We need to find the five  terms of the geometric progression

We know that the nth term formula :

aₙ = a₁rⁿ-¹

where a₁ is first term and r is the common ratio

n is the number of terms

Second term (n=2)

a₂ = 8*$(\frac{5}{2} )^{2-1}$ = $\frac{8*5}{2}$ = 20

Third term (n = 3)

a₃ = 8*$(\frac{5}{2} )^{3-1} = 8*(\frac{5}{2} )^{2} = (\frac{8*25}{4} ) = 50$

Forth term (n=4)

a₄ = $8(\frac{5}{2} )^{4-1} = 8*(\frac{5}{2} )^{3} = (\frac{8*125}{8} ) = 125$

Fifth term (n=5)

a₅ = $8(\frac{5}{2} )^{5-1} = 8*(\frac{5}{2} )^{4} = (\frac{8*625}{16} ) = \frac{625}{2}$

So, five terms are :

8 , 20, 50, 125, 625/2