Geometric Finding Nth Term

Which term has a value of 3/4 given a geometric sequence whose first term is 48 and r = 1/2?

• 5th

• 6th

• 7th

• 8th

Answer explanation

In a geometric sequence, the nth term is given by a_n = a_1 * r^(n-1). Here, a_1 = 48 and r = 1/2. Setting a_n = 3/4, we solve 48 * (1/2)^(n-1) = 3/4, leading to n = 7. Thus, the 7th term is 3/4.

what formula is this?

• For finding the n^th term of an harmonic sequence

• For finding the n^th term of an arithmetic sequence

• For finding the n^th term of an geometric sequence

• For finding the n^th term of an fibonacci sequence

a sequence where each term after the first is obtained by multiplying the preceding term by a nonzero constant called the common ratio (r)

• Arithmetic Sequence

• Geometric Sequence

• Harmonic Sequence

• Fibonacci Sequence

This is one of the example:

5, a₂, a₃, a₄, 3125

the formula that has been used to find the missing term was a₅ = a₁ r⁴.

what sequence where this formula came from?

• Arithmetic Means

• Geometric Means

• Harmonic Means

• Fibonacci Means

Answer explanation

This is one of the example:

5, a₂, a₃, a₄, 3125

the formula is a_{5(this is the order of the last term given)} = a₁ r^{4(This isthe order last missing term given)} .

This type of formula was came from geometric means

What formula is this?

S_n = a₁ - a_nr ÷ 1-r or

S_n = a₁ (1 - rⁿ) ÷ 1 - r

• Sum of an Arithmetic Sequence

• Sum of an Geometric Sequence

• Sum to infinity

• Sum of an Fibonacci Sequence

Which of the following is the formula for finding any term of a geometric sequence?

Identify the 7th term of the sequence: 2, 6, 18, 54, ...

• 1358

• 1338

• 1458

• 1558

The third term of a geometric sequence is 3 and the sixth term is 1/9 . Find the first term.

• 36

• 27

• 18

• 9

What is the common ratio of a geometric sequence whose first and fifth terms are 9 and 144 respectively.

• 5

• 4

• 3

• 2

The number of recruits of a certain association follows a geometric pattern. If they started with only 2 members on the first year and now has 72 recruits on its third year, how many people have they recruited on the second year?

• 8

• 12

• 36

• 50