in a geometric series the fifth term is 27 times the second term and sum of the first two terms is 4. find the geometric series
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2
Answer:
1,3,9,27...
Step-by-step explanation:
Let the geometric series is a, ar, ar², ar³...arⁿ⁻¹
Given that Fifth term is 27 times the second term.
⇒ ar⁴ = 27(ar)
⇒ r³ = 27
⇒ r³ = 3³
⇒ r = 3.
Given that Sum of first two terms is 4.
⇒ a + ar = 4
⇒ a(1 + r) = 4
⇒ a(1 + 3) = 4
⇒ 4a = 4
⇒ a = 1.
When a = 1, r = 3:
a = 1
ar = 3
ar² = 9
ar³ = 27.
Therefore, Geometric series is 1,3,9,27...
Hope it helps!
siddhartharao77:
:-)
Answered by
0
Step-by-step explanation:
Let the geometric series is a, ar, ar², ar³...arⁿ⁻¹
Given that Fifth term is 27 times the second term.
⇒ ar⁴ = 27(ar)
⇒ r³ = 27
⇒ r³ = 3³
⇒ r = 3.
Given that Sum of first two terms is 4.
⇒ a + ar = 4
⇒ a(1 + r) = 4
⇒ a(1 + 3) = 4
⇒ 4a = 4
⇒ a = 1.
When a = 1, r = 3:
a = 1
ar = 3
ar² = 9
ar³ = 27.
Therefore, Geometric series is 1,3,9,27...
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