Question

The 1st and the 8th term of a GP are 4 and 512 respectively. Find: (i) the common ratio (ii) the sum of its first 5 terms. [

Answer 1

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Answer 2

Answer:

(i) Common Ratio, r=2

(ii) Sum of 5 term = 124

Step-by-step explanation:

The 1st and the 8th term of a GP are 4 and 512 respectively.

(i) Using GP formula,

$a_n=ar^{n-1}$

[tex[a_1=a=4[/tex]

$a_8=4(r)^{8-1}$

$512=4(r)^7$

$2^7=r^7$

hence, r=2

Thus, Common Ratio, r=2

(ii) Sum of first 5 term

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

Where, a=4, r=2 and n=5

$S_5=\frac{4(2^5-1)}{2-1}$

$S_5=124$

Sum of first 5 term of GP is 124