Find the sum to 40 terms of the arithmetic sequence below. Please show your
work.
14+23+32

7580

Step-by-step explanation:

The formula for the sum of an arithmatic sequence is

,

where n = total number of terms (in this case 40)

= the first term (in this case 14)

and = the last term (we will need to find this)

to find the last term, we can use this formula:

where d is the difference between each term (in this case 9, because 23 - 14 = 9, and 32 - 23 = 9)

thus, = 14 + (40 - 1)9 = 14 + 39*9 = 14 + 351 = 365

plug this back into the first formula to get

Σ = (14 + 365) = 20(379) = 7580

14

step-by-step explanation:

c. 27 units.

step-by-step explanation:

we are told that in circle a, ∠bae ≅ ∠dae.

we can see from our given diagram that in and ;

, as these are radii of our given circle.

therefore, by sas congruence postulate.

hence, side be will be equal to side de as corresponding parts of congruent triangles are congruent. so we can set an equation to find the value of x as:

now let us substitute x=17 in the expression for the length of be.

therefore, length of be will be 27 units and option c is the correct choice.