How to sum values in multiple rows to a new column in R?

My dataframe:

structure(list(Observation = c("Apple", "Blueberry", "Cirtus", 
"Dates", "Eggplant"), Topic = 1:5, Gamma = c(0.1, 0.1, 0.2, 0.2, 
0.1)), class = "data.frame", row.names = c(NA, -5L))

  Observation Topic Gamma
1       Apple     1   0.1
2   Blueberry     2   0.1
3      Cirtus     3   0.2
4       Dates     4   0.2
5    Eggplant     5   0.1

How can I tell R to add the values of 1, 3, and 5, and 2 and 4, and then save it in a new column? For example:

Observation	Topic	Gamma	new variable
Apple	1	.10	.40
Blueberry	2	.10	.30
Cirtus	3	.20	.40
Dates	4	.20	.30
Eggplant	5	.10	.40

Essentially, I'd like each observation to have a new value that sums up the gamma scores of topics 1, 3, and 5, as well as topics 2 and 4.

Update: Clarification: I am not trying to add even topic numbers or odd topic numbers. Sometimes it will be a mixture of both. See this new table as an example:

Observation	Topic	Gamma	new variable
Apple	1	.10	.10
Blueberry	2	.10	.70
Cirtus	3	.20	.40
Dates	4	.20	.40
Eggplant	5	.10	.70
Fruits	6	.50	.70

In this example, I left topic 1 alone, added topics 2, 5, and 6, and added topics 3 and 4.

Update: Clarification:

Observation	Topic	Gamma	new variable
Apple	1	.10	.10
Apple	2	.10	.70
Apple	3	.20	.40
Apple	4	.20	.40
Apple	5	.10	.70
Apple	6	.50	.70
Blueberry	1	.20	.20
Blueberry	2	.10	.60
Blueberry	3	.30	.80
Blueberry	4	.50	.80
Blueberry	5	.40	.60
Blueberry	6	.10	.60

In this example, Each fruit (observation) has their own set of values for each topic and I summed the same topics as listed above (2, 5, and 6, 3 and 4) per fruit.

Solution

Update II on new request:

library(dplyr)

df %>% 
  group_by(Observation, grp = case_when(Topic %in% 1 ~ 1,
                           Topic %in% c(2,5,6) ~ 2,
                           Topic %in% c(3,4) ~ 3)) %>% 
  mutate(new_variable = sum(Gamma)) %>% 
  ungroup %>% 
  select(-grp)

  Observation Topic Gamma new_variable
   <chr>       <int> <dbl>        <dbl>
 1 Apple           1   0.1          0.1
 2 Apple           2   0.1          0.7
 3 Apple           3   0.2          0.4
 4 Apple           4   0.2          0.4
 5 Apple           5   0.1          0.7
 6 Apple           6   0.5          0.7
 7 Blueberry       1   0.2          0.2
 8 Blueberry       2   0.1          0.6
 9 Blueberry       3   0.3          0.8
10 Blueberry       4   0.5          0.8
11 Blueberry       5   0.4          0.6
12 Blueberry       6   0.1          0.6

Update: on new request of OP. This solution is inspired fully by PaulS solution (credits to him):

library(dplyr)

df %>% 
  group_by(grp = case_when(Topic %in% 1 ~ 1,
                           Topic %in% c(2,5,6) ~ 2,
                           Topic %in% c(3,4) ~ 3)) %>% 
  mutate(new_variable = sum(Gamma)) %>% 
  ungroup %>% 
  select(-grp)

  Observation Topic Gamma new_variable
  <chr>       <int> <dbl>        <dbl>
1 Apple           1   0.1          0.1
2 Blueberry       2   0.1          0.7
3 Cirtus          3   0.2          0.4
4 Dates           4   0.2          0.4
5 Eggplant        5   0.1          0.7
6 Fruits          6   0.5          0.7

First answer: We could sum Gamma after identifying odd and even rows in an ifelse statement: In this case row_number could be replaced by Topic

library(dplyr)

df %>% 
  mutate(new_variable = ifelse(row_number() %% 2 == 1, 
                               sum(Gamma[row_number() %% 2 == 1]), # odd 1,3,5
                               sum(Gamma[row_number() %% 2 == 0])) # even 2,4
         )

  Observation Topic Gamma new_variable
1       Apple     1   0.1          0.4
2   Blueberry     2   0.1          0.3
3      Cirtus     3   0.2          0.4
4       Dates     4   0.2          0.3
5    Eggplant     5   0.1          0.4

data:

structure(list(Observation = c("Apple", "Blueberry", "Cirtus", 
"Dates", "Eggplant"), Topic = 1:5, Gamma = c(0.1, 0.1, 0.2, 0.2, 
0.1)), class = "data.frame", row.names = c(NA, -5L))

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