Question

if the 5th and the 10th terms of a g. p are 32 and 1024 respectively find the first term and the common ratio​

Answer 1

Answer:

a=2

r=2

Step-by-step explanation:

Let first term of the GP be a and its common ratio be r.

5th term = a₅ = ar⁵⁻¹=ar⁴=32    .........(1)

10th term = a₁₀ = ar¹⁰⁻¹=ar⁹=1024    .....(2)

Dividing (2) by (1), we get,

ar⁹/ar⁴=1024/32

=>r⁵=32

=>r=2

so, from (1), we get,

ar⁴=32

=>a(2)⁴=32

=>a=32/16

=>a=2

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Answer 2

Answer:

a=2

r=2

Let first term of the GP be a and its common ratio be r.

5th term = a₅ = ar⁵⁻¹=ar⁴=32    .........(1)

10th term = a₁₀ = ar¹⁰⁻¹=ar⁹=1024    .....(2)

Dividing (2) by (1), we get,

ar⁹/ar⁴=1024/32

=>r⁵=32

=>r=2

so, from (1), we get,

ar⁴=32

=>a(2)⁴=32

=>a=32/16

=>a=2

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