Given an arithmetic progression with u21 = 65 and d = -2, find the value of the first term.

The value of the first term is 105

The nth term of an arithmetic sequence is gotten by using the formula:

= a + (n - 1)d

The value of the 21st term which has been given in the question is 65 and the common difference is -2. This will be:

a + (n - 1)d = 65

a + (21 - 1)d = 65

a + 20d = 65

Since d, common difference = -2

a + 20d = 65

a + 20(-2) = 65

a - 40 = 65

a = 60 + 45

a = 105

In conclusion, the value of the first term is 105

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105 = a

Step-by-step explanation:

L = a + (n-1)*d

n = 65

d = -2

L = u21 = 65

65 = a + (21 - 1)*(-2)        Divide by - 2

65 = a + 20*-2               Multiply 20 times - 2

65 = a  - 40                    Add 40 to both sides

65+40 = a                      Combine

105 = a

a box 3 3/4 feet long or 4+ feet.

step-by-step explanation: