Writing and Using Explicit Rules for Arithmetic Sequences

Let's use the formula for the

n

th term of

n

a_{n} = a_{1} + (n - 1) d

Since we know the common difference

d = - 5

and

a_{12} = 22,

we can substitute

- 5

for

d,

12

for

n,

and

22

for

a_{n} .

22 = a_{1} + (12 - 1) (- 5)

Since

a_{1}

is the only unknown value left, we can can calculate its value.

22 = a_{1} + (12 - 1) (- 5)

SubTermSubtract term

22 = a_{1} + (11) (- 5)

a (- b) = - a \cdot b

22 = a_{1} + (- 55)

LHS + 55 = RHS + 55

77 = a_{1}

RearrangeEqnRearrange equation

a_{1} = 77

The first term equals

77 .

Writing and Using Explicit Rules for Arithmetic Sequences 1.11 - Solution