Question

The first term of g.p is 375 and 4th term is 192. Find common ratio and sum of the first 14 terms

Answer 1

Answer:

r = 4/5 = 0.8

Sum of first 14 terms = 1875 × ( 1 - (4/5)^14 )  (exactly)

≈ 1792.54  (approximately)

Step-by-step explanation:

First term is a₁ = 375

n-th term is aₙ = a₁ r^(n-1)

So 4th term is

192 = a₄ = a₁ r³ = 375 r³

=>  r³ = 192 / 375 = 64 / 125 = 4³/5³

=>  r = 4/5

------------

a₁ + a₂ + a₃ + ... + a_14

= a₁ × ( 1 + r + r² + ... + r^13 )

= a₁ × ( 1 - r^14 ) / ( 1 - r )

= 375 × ( 1 - (4/5)^14 ) / ( 1 - 4/5 )

= 375 × ( 1 - (4/5)^14 ) / ( 1/5 )

= 375 × 5 × ( 1 - (4/5)^14 )

= 1875 × ( 1 - (4/5)^14 )

≈ 1792.54

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