Question

HELPP! Calculate S22 for the arithmetic sequence in which a12=2.4 and the common difference is d=3.4

Answer 1

Answer:

Option A is correct.

Value of $S_{22} = 15.4$

Step-by-step explanation:

Given: $a_{12} = 2.4$ 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;

$S_n =\frac{n}{2}(2a+(n-1)d)$, 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 ;

$a_n = a+(n-1)d$                             ......[2]

First find a.

it is given that $a_{12} = 2.4$

Put n =12 and d=3.4 in equation [2] we have;

$a_{12} = a+(12-1)(3.4)$

$a_{12} = a+(11)(3.4)$

2.4 = a + 37.4

Simplify:

a = - 35

Now, to calculate $S_{22}$

we use equation [1];

here, n =2 , a =-35 and d=3.4

$S_{22} = \frac{22}{2}(2(-35)+(22-1)(3.4))$

$S_{22} = (11)(-70+21(3.4))$

$S_{22} = (11)(-70+71.4)$

$S_{22} = (11)(1.4)$

Simplify:

$S_{22} = 15.4$

Therefore, the sum of sequence of 22nd term i.e, $S_{22} = 15.4$

Answer 2

Answer:

A. 15.4

Step-by-step explanation: