MATH SOLVE

3 months ago

Q:
# An arithmetic sequence has first term a = 5 and common difference d = 4. how many terms of this sequence must be added to get 4185?

Accepted Solution

A:

Given that in arithmetic sequence a=5 and common difference, d=4. Thus the number of terms of this sequence that must be added to attain 4185 will be found as follows:

the explicit formula for arithmetic sequence is given by:

sn=n/2(2a+(n-1)d)

where n is the number of terms:

thus plugging in the values we get:

4185=n/2(2*5+(n-1)4)

solving for n we get:

8370=(10+4n-4)

8370=(6+4n)

4n=8364

n=8364/4

n=2091

thus the number of terms will be:

2091

Β Β

the explicit formula for arithmetic sequence is given by:

sn=n/2(2a+(n-1)d)

where n is the number of terms:

thus plugging in the values we get:

4185=n/2(2*5+(n-1)4)

solving for n we get:

8370=(10+4n-4)

8370=(6+4n)

4n=8364

n=8364/4

n=2091

thus the number of terms will be:

2091

Β Β