Answer:
Option A is correct.
Value of [tex]S_{22} = 15.4[/tex]
Step-by-step explanation:
Given: [tex]a_{12} = 2.4[/tex] and common difference(d) = 3.4
A sequence of numbers is arithmetic i.e, it increases or decreases by a constant amount each term.
The sum of the nth term of a arithmetic sequence is given by;
[tex]S_n =\frac{n}{2}(2a+(n-1)d)[/tex], where n is the number of terms, a is the first term and d is the common difference.
We also know the nth tern sequence formula which is given by ;
[tex]a_n = a+(n-1)d[/tex] ......[2]
First find a.
it is given that [tex]a_{12} = 2.4[/tex]
Put n =12 and d=3.4 in equation [2] we have;
[tex]a_{12} = a+(12-1)(3.4)[/tex]
[tex]a_{12} = a+(11)(3.4)[/tex]
2.4 = a + 37.4
Simplify:
a = - 35
Now, to calculate [tex]S_{22}[/tex]
we use equation [1];
here, n =2 , a =-35 and d=3.4
[tex]S_{22} = \frac{22}{2}(2(-35)+(22-1)(3.4))[/tex]
[tex]S_{22} = (11)(-70+21(3.4))[/tex]
[tex]S_{22} = (11)(-70+71.4)[/tex]
[tex]S_{22} = (11)(1.4)[/tex]
Simplify:
[tex]S_{22} = 15.4[/tex]
Therefore, the sum of sequence of 22nd term i.e, [tex]S_{22} = 15.4[/tex]
