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?

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

General Equation : an = a1 + d (n - 1)

Find the nth sequence:

Given that a1 = 5 and d = 4,

an = 5 + 4 (n - 1)

an = 5 + 4n - 4

an = 4n + 1

Find an:

Given that Sn = 4185, find an

sn = (a + an) / 2

4185 = (5 + an) / 2

5 + an = 8370

an = 8370 - 5

an = 8365

Find n:

We know that an = 8365, find n

an = 4n + 1

8365 = 4n + 1

4n = 8365 - 1

4n = 8364

n = 2091

Answer: 2091 terms