Find the 6th term in the geometric sequence with t3 = 150 and t5 = 3750.

The 6th term in the geometric sequence is either 18750 or -18750.

Step-by-step explanation:

Given information: In the given GP

The nth term of a GP is

where, a is first term and r is common ratio.

Third term of the GP is 150, so

         .... (1)

Fifth term of the GP is 3750, so

         .... (2)

Divide equation (2) by equation (1).

The value of common ratio is either 5 or -5.

Put the value of r² in equation (1).

The first term of the GP is 6.

If the first term of GP is 6 and common difference is 5, then 6th term is

If the first term of GP is 6 and common difference is -5, then 6th term is

Therefore the 6th term in the geometric sequence is either 18750 or -18750.

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step-by-step explanation: