If the 2nd and 5th terms of a G.P are 6 and 48 respectively, find the sum of the first four for term

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1. 

   MR BOLAJI June 29, 2025

   Step 1: General formula of a G.P.

   The general term of a G.P. is:

   $T_n=a{r}^{n-1}$Tn​=arn−1

   Where:

   • $a$a = first term

   • $r$r = common ratio

   • $T_n$Tn​ = nth term.

   ep 2: Use given terms

   • 2nd term: $ar=6$ar=6 → (1)

   • 5th term: $a{r}^4=48$ar4=48 → (2)

   Divide (2) by (1):

   $\frac{a{r}^4}{ar}=\frac{48}{6}\Rightarrow r^3=8\Rightarrow r=2$arar4​=648​⇒r3=8⇒r=2

   Now substitute $r=2$r=2 into equation (1):

   $a\left(2\right)=6\Rightarrow a=3$a(2)=6⇒a=3

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   Step 3: Find the first four terms

   Using $a=3$a=3, $r=2$r=2:

   • 1st term: $a=3$a=3

   • 2nd term: $ar=6$ar=6

   • 3rd term: $a{r}^2=12$ar2=12

   • 4th term: $a{r}^3=24$ar3=24

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   Step 4: Sum the first four terms

   $S=3+6+12+24=45$S=3+6+12+24=45

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   ✅ Final Answer:

   $\boxed{{\displaystyle 45}}$45​

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