Question

Given the following terms of a geometric sequence.
a6= 3159 , a13 = 6908733
Determine: a1 = , r=​

Answer 1

I'm sorry but i don't know

Answer 2

Answer:

a1 = 13, r = 3

Step-by-step explanation:

Given:- a6= 3159 , a13 = 6908733

To Find:- Value of a1 and r.

Solution:-

Geometric Progression or GP is a type of sequence where each succeeding term is produced by multiplying each preceding term by a fixed number, which is called a common ratio.

So, 2nd term = 1st term × common ratio

a2 = a1 × r

Given that a6 = 3159, a13 = 6908733

a13 = a12 × r

     = (a11 × r) × r

     = (a10 × r) × r×r

     = (a9 × r) ×r×r×r

     = (a8 × r) ×r×r×r×r

     = (a7 × r) ×r×r×r×r×r

     = (a6 × r) ×r×r×r×r×r×r

⇒ a13  = a6 × $r^{7}$

⇒ 6908733 = 3159 × $r^{7}$

⇒ $r^{7}$ = 6908733 ÷ 3159

⇒ $r^{7}$ = 2187

⇒ $r^{7}$ = $3^{7}$

⇒ r = 3.

Now, a6 = a5 × r = a1 × $r^{5}$

⇒ a6 = a1 × $r^{5}$

⇒ 3159 = a1 × $3^{5}$

⇒ a1 = 3159 ÷ $3^{5}$

⇒ a1 = 3159 ÷ 243

⇒ a1 = 13.

Therefore, a1 = 13 and r = 3.

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