Answer:
Therefore, the value of S11 in the arithmetic sequence with a = 2.5, d = 1.5, and n = 11 is 110.
Explanation:
In an arithmetic sequence, each term is obtained by adding a constant difference to the previous term. The formula to find the value of any term in an arithmetic sequence is given by:
an = a + (n - 1)d
Where:
an represents the value of the nth term,
a represents the first term,
n represents the position of the term in the sequence, and
d represents the common difference.
In this case, we are given that a = 2.5, d = 1.5, and n = 11. Let's substitute these values into the formula to find the value of a11:
a11 = 2.5 + (11 - 1) * 1.5
= 2.5 + 10 * 1.5
= 2.5 + 15
= 17.5
Therefore, the value of a11 in the arithmetic sequence with a = 2.5, d = 1.5, and n = 11 is 17.5.
Now let's calculate S11, which represents the sum of the first 11 terms in the arithmetic sequence. The formula to find the sum of an arithmetic sequence is given by:
Sn = (n/2)(2a + (n - 1)d)
Where:
Sn represents the sum of the first n terms.
Substituting the given values into this formula, we can find S11:
S11 = (11/2)(2 * 2.5 + (11 - 1) * 1.5)
= (11/2)(5 + 10 * 1.5)
= (11/2)(5 + 15)
= (11/2)(20)
= (11 * 20)/2
= 220/2
= 110