We are given two terms of an arithmetic sequence.

a_{4} = - 2.4 and a_{6} = 2

With the information provided, we want to find the common difference

d

and the first term

a_{1} .

Recall that the common difference is the difference between any two consecutive terms. Since the terms we are given are not consecutive, we will divide their difference by the difference of their positions.

d = \frac{a _{6} - a _{4}}{6 - 4}

SubstituteII

$a_{6} = 2$ , $a_{4} = - 2.4$

d = \frac{2 - ( - 2 . 4 )}{6 - 4}

▼

Evaluate right-hand side

SubNeg

$a - (- b) = a + b$

d = \frac{4 . 4}{2}

CalcQuot

Calculate quotient

d = 2.2

Now that we know that

d = 2.2,

we can write a partial equation of the explicit formula for our arithmetic sequence.

a_{n} = a_{1} + (n - 1) d ⇕ a_{n} = a_{1} + (n - 1) (2.2)

We will use this formula to find the first term

a_{1} .

To do so, we can use any of the given terms. Let's use

a_{6} = 2 .

Be aware that for this term the value of

n

is

6 .

a_{n} = a_{1} + (n - 1) (2.2)

Substitute

$n = 6$

a_{6} = a_{1} + (6 - 1) (2.2)

▼

Simplify

SubTerms

Subtract terms

a_{6} = a_{1} + 5 (2.2)

Multiply

a_{6} = a_{1} + 11

Substitute

$a_{6} = 2$

2 = a_{1} + 11

▼

Solve for

a_{1}

SubEqn

$LHS - 11 = RHS - 11$

- 9 = a_{1}

RearrangeEqn

Rearrange equation

a_{1} = - 9

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