Question

Find the gp if s10 :s5 =33:1 and t6 =32

Answer 1

Answer:

1,2,4,8,16,32, .......

Step-by-step explanation:

Sum of n terms of an G.P. having first term a and common ratio r is given by

$S_{n}= a\frac{r^{n}-1 }{r-1}$ ..... (1).

So, $\frac{S_{10} }{S_{5} } =\frac{r^{10}-1 }{r^{5}-1 } =33 (Given)$

⇒ $r^{5}+1=33$

⇒ $r^{5} =32$..... (2)

⇒ r=2

Now, also given that $t_{6}=ar^{5}=32$, ⇒a(32)=32 {From equation (2)}

⇒ a=1

Hence, the G.P. will be 1,2,4,8,16,32,  .....  (Answer)