Arithmetic_Mixed_Problems (Practice Exercises)

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Formula:

Arithmetic Sequence

The nth term of an arithmetic sequence:

Un = U1 + (n - 1) d

The sum of n terms of an arithmetic sequence:

Sn = n/2 (2 U1 + (n - 1) d)

Sn = n/2 (U1 + Un)

The first term of an arithmetic sequence is -8 and the common difference is 3.

(a) Find the seventh term of the sequence.

(b) The last term is 100. How many terms are there?

U1 = -8

d = 3

Un = 100

(a) Un = U1 + (n - 1) d

U7 = -8 + (7 - 1) 3

U7 = 10

(b) Un = U1 + (n - 1) d

100 = -8 + (n - 1) 3

100 = -8 + 3n - 3

100 = -11 + 3n

111 = 3n

n = 37