Question

Find the first term and the common ratio of a G.P whose fourth term is 250 and seventh
term is 31,250
2,5
2/5,25
1,16
4,5/3​

Answer 1

Hope this will be helpful

Answer 2

The first term is 2 and the common ratio of GP is 5.

Option first is correct.

Step-by-step explanation:

We have been given that

a₄ = 250

a₇ = 31250

The nth term of a GP is given by

$a_n=ar^{n-1}$

Substitute n = 4

$a_4=ar^{4-1}\\\\250=ar^3...(i)$

Substitute n = 7

$a_7=ar^{7-1}\\\\31250=ar^6...(ii)$

Divide equation (ii) by (i)

$\frac{31250}{250}=r^3\\\\r^3=125\\\\r=5$

Substituting this value in (i)

$250=a(5)^3\\\\250=125a\\\\a=2$

Therefore, the first term is 2 and common ratio of GP is 5.

#Learn More:

The fourth term of a g.p is the square of its second term and the first term is -3. Determine it's seventh term

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