Question

Let bn be a geometric sequence such that b2 = 14 and bz= 235298. Put by in the standard form, i.e., in the form bn= brⁿ－¹

Answer 1

To find the standard form of the geometric sequence bn = brⁿ⁻¹, we need to determine the first term b1 and the common ratio r using the given terms b2 = 14 and bz = 235298, and then express bn with b1 and r.

Step-by-step explanation:

To express the geometric sequence in the standard form bn = brⁿ⁻¹, we need to find the common ratio r and the first term b1. Given the terms b2 = 14 and bz = 235298 (assuming 'z' is a typo and should be interpreted as another term in the sequence, such as 'n'), let's follow the steps to find these values:

1. Write down the formula for the nth term of a geometric sequence, which is bn = b1 × rⁿ⁻¹.
2. Using the given terms, set up two equations: b2 = b1 × r and bz = b1 × r⁺⁻¹ (where 'z' represents the position of 235298 in the sequence).
3. Solve these two equations simultaneously to find the values of b1 and r.
4. Once b1 and r are known, use them to write the general formula for the nth term of the sequence: bn = b1 × rⁿ⁻¹.

This will give us the standard form requested for the sequence by.