Question

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

Answer 1

A. 15.4

Explanation:

Answer 2

Option A is correct.

Value of
`S_(22) = 15.4`

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 =(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) = (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`