Murtha has decided to start a pebble collection. She collects one pebble the first day and two pebbles on the second day. On each subsequent day she collects one more pebble than the previous day. How many pebbles will she have collected at the end of the twelfth day

78

Step-by-step explanation:

Given that:

First day (a) = 1

1 more pebble every subsequent day than the previous day

Tn = a + (n - 1)d

d = common difference ; difference between pebbles in two successive days = 1

n = nth day

At the end of the 12th day;

Tn = a + (n - 1)d

T(12) = 1 + (12 - 1) 1

T(12) = 1 + 11

T(12) = 12

Appling the sun if arithmetic progression formula : Sum of AP:

n/2 (a + Tn)

n = number of terms

12/2 (1 + 12)

6(13)

= 78

OPTION A

OPTION C

Step-by-step explanation:

A relation becomes a function when it satisfies the following two conditions:

(i) Any element from the domain can only be mapped to only element in the co-domain.

(ii) No element in the domain should be left unmapped.

Note that an element in the co-domain need not have a pre - image.

OPTION A: Every element has an image and no element is mapped to two different elements on the co - domain. so, it is a function.

OPTION B: The element 9 is mapped to both 4 and 6. Condition (1) is not satisfied. So, it is not a function.

OPTION C: Both the conditions of a function are satisfied. So, OPTION C is a function. Note that the element 8 in the co - domain does not have a pre - image but it is still a function.

OPTION D: Element 1 in the domain is mapped to two elements. Violation of Condition (i). So, it is not a function.