the ninth term of an arithmetic sequence is 23 and the 33rd term of the sequence is -241 , calculate the sume of the first 15 terms of the sequence , using the formula

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

a+8d = 23

a+32d = -241
subtract them ...
24d = -264
d = -11
back into the first ....
a - 88 = 23
a = 111

now that we know a = 111, d = -11 and n = 15
just plug those values into your formula

Sn=510

S15 =510

To find the sum of the first 15 terms of an arithmetic sequence, we need to have information about the first term (a), the common difference (d), and the number of terms (n). However, in this case, we only have information about the 9th term and the 33rd term.

To find the first term (a) and the common difference (d) of the arithmetic sequence, we can use the formulas:

a = nth term - (n - 1) * d
d = (nth term - a) / (n - 1)

Let's calculate a and d using the given information:

Given: 9th term = 23 and 33rd term = -241

Using the first formula:
a = 23 - (9 - 1) * d
a = 23 - 8d

Using the second formula:
-241 = a + 32d

Now we have two equations:

a = 23 - 8d
a + 32d = -241

Solving these two equations simultaneously will give us the values of a and d.

Once we have the values of a and d, we can substitute them into the formula for the sum of the first 15 terms:

s = 15(2a + (15 - 1)d) / 2

Now let's solve the equations and calculate the sum.