Question

Если an=3n+2 найти s18-?

Answer 1

A1=5; a18=56 ;n=18

S18=a1+an/2•n=549

Answer 2

To find the value of s18 in the sequence an=3n+2, we need to find the 18th term in the sequence and then subtract it from the sum of the first 18 terms.

The formula for the nth term (an) of the arithmetic sequence is given as:

an = a1 + (n-1) * d

where a1 is the first term and d is the common difference.

In this case, we have a1 = 3(1) + 2 = 5 (since n=1), and the common difference d = 3.

Now, let's find the value of s18, which is the sum of the first 18 terms of the sequence:

s18 = (n/2) * (a1 + a18)

Substitute the known values:

s18 = (18/2) * (5 + a18)

We still need to find the value of a18. We can use the formula for the nth term:

a18 = 3(18) + 2 a18 = 54 + 2 a18 = 56

Now we can calculate s18:

s18 = (18/2) * (5 + 56) s18 = 9 * 61 s18 = 549

Therefore, s18 - 549.