Question

The third term of a Go is 9 and the fifth term is 16 find the 4th term and the sum of the first four terms

Answer 1

9 * r^2 = 16 ... r^2 = 16/9 ... r = ± 4/3

Answer 2

a ar ar^2 ....a r^(n-1)

a r^2 = 9
a r^4 = 16

a = 16/r^4 = 9/r^2
16/9 = r^2
r = 4/3
then a = 9/(16/9) = 81/16
check
ar^4 = 81/16 * (16*16 / 9*9 ) = 16 sure enough
so
a r^3 = fourth term = 81/16 * (4^3/3^3)
= (81/16)(16*4 / 9*3)= 3*4 = 12

Answer 3

for sum of first n terms google math is fun geometric sequence

a (1-r^n) / (1-r)
a = 81/16
r = 4/3
n = 4
so
(81/16) [ 1 - (4/3)^4 ] / [ 1 - (4/3) ]

Answer 4

[AI-generated answer — Explain Bot]

To find the fourth term, we need to identify the pattern or relationship between the given terms. Let's examine the difference between consecutive terms:

Difference between the 3rd and 5th terms: 16 - 9 = 7
The difference between consecutive terms is constant at 7.

If we continue this pattern, the difference between the 1st and 3rd term would also be 7, as the 3rd term is 9. Therefore, the 1st term is 9 - 7 = 2.

Now, we can find the 4th term by adding the difference to the 3rd term:

3rd term: 9
Difference between terms: 7

4th term = 3rd term + Difference = 9 + 7 = 16

The fourth term of the sequence is 16.

To calculate the sum of the first four terms, we need to add them together:

1st term: 2
2nd term: ?
3rd term: 9
4th term: 16

Sum of the first four terms = 1st term + 2nd term + 3rd term + 4th term = 2 + ? + 9 + 16

Since we know that the difference between terms is 7, the 2nd term would be 3rd term - Difference = 9 - 7 = 2.

Substituting the values, we get:

Sum of the first four terms = 2 + 2 + 9 + 16 = 29

Therefore, the sum of the first four terms is 29.