The Nth Term Of A Sequence Is Given By Tn=7n−3. How Many Terms Of The Sequence Are Less Than 300? What Is The Value Of The First term greater than 300 ?

Question

asked Jun 20, 2024 134k views

1 Answer

Uyetch · Answer 1 · 2024-06-24T14:49:02+0000

The number of terms less than 300 is 43 and the first term greater than 300 is 305.

To find the number of terms in the sequence that are less than 300, we can set up the inequality:

7n - 3 < 300

We can then solve for n:

7n < 303

n < 43.29

Since n represents the number of terms in the sequence and cannot be a decimal, the number of terms that are less than 300 is 43.

To find the first term greater than 300, we substitute n = 44 into the nth term formula:

T44 = 7(44) - 3

T44 = 305

Therefore, the value of the first term greater than 300 is 305.