Learning resource: Grade 10 Patterns and Practicalities.

3. Example 15: Find the sum of multiples of 4 from 1 to 100.
Recall: Multiples of 4 are 4, 8, 12, 16,…
We can use either of the two formula:
𝑆 𝑛 =
𝑛
2
(𝑎1 + 𝑎 𝑛) 𝑆 𝑛 =
𝑛
2
[(2𝑎1 + 𝑛 − 1 𝑑]
Given are: a1 = 4, an = 100, d = 4
RFT: Sn but n = ?
𝒂 𝒏 = 𝒂 𝟏 + 𝒏 − 𝟏 𝒅
𝟏𝟎𝟎 = 𝟒 + 𝒏 − 𝟏 𝟒
𝟏𝟎𝟎 = 𝟒 + 𝟒𝒏 − 𝟒
𝟏𝟎𝟎 = 𝟒𝒏
𝟐𝟓 = 𝒏
𝑺 𝟐𝟓 =
𝒏
𝟐
(𝒂 𝟏 + 𝒂 𝒏)
𝑺 𝟐𝟓 =
𝟐𝟓
𝟐
(𝟒 + 𝟏𝟎𝟎)
𝑺 𝟐𝟓 =
𝟐𝟓
𝟐
(𝟏𝟎𝟒)
𝑺 𝟐𝟓 = 𝟏𝟑𝟎𝟎
Therefore, the sum of
multiples of 4 from 1 to
100 is 1300.

4. Example 16: Allan saved Php 10 on Monday, Php 11 on Tuesday,
Php 12 on Wednesday and so on. How much will he save in 30
days?
Given are: a1 = 10, n = 30, d = 1
RTF: S30, but we have to find first an
:
1
10,
2
11,
3
12,…
30
?
𝒂 𝒏 = 𝒂 𝟏 + 𝒏 − 𝟏 𝒅
𝒂 𝒏 = 𝟏𝟎 + 𝟑𝟎 − 𝟏 𝟏
𝒂 𝒏 = 𝟏𝟎 + 𝟐𝟗
𝒂 𝒏 = 𝟑𝟗
𝑺 𝟑𝟎 =
𝒏
𝟐
(𝒂 𝟏 + 𝒂 𝒏
𝑺 𝟑𝟎 =
𝟑𝟎
𝟐
(𝟏𝟎 + 𝟑𝟗)
𝑺 𝟑𝟎 = 𝟕𝟑𝟓
Therefore, Allan
can save up to Php
735 after 30 days.

5. Example 16: In a country experiencing runaway inflation, the
cost of kilo of rice increased 50 cents a day. On March 1, a kilo
of rice costs Php 22.
a. Give the cost of a kilo of rice on March 30 of the same year.
b. Suppose your family bought a kilo of rice each day. How
much would your family have spent on rice from March 1 to
May 30?