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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

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Answer:

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

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