Calculate S_22 for the arithmetic sequence in which a_12=2.4 and the common difference is d=3.4

Answer 1

To calculate the 22nd term of an arithmetic sequence, we can use the formula:

a_n = a_1 + (n-1)d

where a_n is the nth term, a_1 is the first term, n is the position of the term, and d is the common difference.

In this case, a_12 = 2.4 and d = 3.4. We want to find a_22.

a_n = a_1 + (n-1)d
a_22 = a_1 + (22-1)d
a_22 = a_1 + 21d

To find a_1, we can use the formula:

a_n = a_1 + (n-1)d
a_12 = a_1 + (12-1)d
2.4 = a_1 + 11d

We can rearrange this equation to solve for a_1:

a_1 = 2.4 - 11d

Substituting this value of a_1 into the equation for a_22:

a_22 = (2.4 - 11d) + 21d
a_22 = 2.4 + (21d - 11d)
a_22 = 2.4 + 10d

Now we can calculate a_22 using the value of d:

a_22 = 2.4 + 10(3.4)
= 2.4 + 34
= 36.4

Therefore, S_22 = 36.4.