How to answer these using geometric progression formula ?

Given the third term and the fourth term for a geometric progression is #75 and 375# respectively. Find the sum of the first seven terms after the third term

Answer 1

#7324125#

#"using the following formulae"#
#•color(white)(x)a_n=ar^(n-1)#
#•color(white)(x)S_n=(a(r^n-1))/(r-1)#
#a_3=ar^2=75to(1)#
#a_4=ar^3=375to(2)#
#"divide equation "(2)" by equation "(1)#
#(ar^3)/(ar^2)=375/75rArrr=5#
#"substitute "r=5" in equation "(1)#
#rArr25a=75rArra=3#
#"sum of "a_4toa_(10)=S_(10)-S_3#
#=(3(5^(10)-1))/4-(3(5^3-1))/4#
#=7324218-93=7324125#
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Answer 2

To answer questions using the geometric progression formula, follow these steps:

  1. Find the common ratio (r): Divide any term by the preceding term to find the common ratio.

  2. Determine the nth term (Tn): Use the formula Tn = a * r^(n-1), where "a" is the first term and "n" is the term number.

  3. Find the sum of the first n terms (Sn): Use the formula Sn = a * (1 - r^n) / (1 - r), where "a" is the first term and "n" is the number of terms.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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