Porisma

Worked solution

Check the first term and common difference

The source AP table lists 2,7,12,17,222,7,12,17,22; 13,10,7,4,113,10,7,4,1; and −14,−11,−8,−5,−2-14,-11,-8,-5,-2. Complete the first-term aa and common-difference dd entries. The following printed question asks: is 2,−4,6,−8,102,-4,6,-8,10 an arithmetic progression?

CJC · Sequences and Series · AP table and question (unnumbered)

Source table: 2,7,12,17,22

Answer

a=2a=2, d=5d=5.

Read the first term and subtract consecutive terms

a=2,d=(7)−(2)=5a=2,\qquad d=(7)-(2)=5

These complete the two source-table columns.

How did this part go?

Source table: 13,10,7,4,1

Answer

a=13a=13, d=−3d=-3.

Read the first term and subtract consecutive terms

a=13,d=(10)−(13)=−3a=13,\qquad d=(10)-(13)=-3

These complete the two source-table columns.

How did this part go?

Source table: -14,-11,-8,-5,-2

Answer

a=−14a=-14, d=3d=3.

Read the first term and subtract consecutive terms

a=−14,d=(−11)−(−14)=3a=-14,\qquad d=(-11)-(-14)=3

These complete the two source-table columns.

How did this part go?

The unnumbered question

Answer

No; the sequence is not an arithmetic progression.

Compare two consecutive differences

(−4)−2=−6,6−(−4)=10≠−6(-4)-2=-6,\qquad6-(-4)=10\ne-6

The printed Teacher answer rules out a common difference.

How did this part go?

Solution notes

The three table rows and following unnumbered question are retained together; the part labels organise the activity and are not printed mark allocations.