Question

HURRYYYYYWhat is the first term in the sequence for which d = -2 and a7 = 3?

a.
-6
c.
15
b.
12
d.
-12

Answer 1

`\huge \boxed{a_1=15 }}`

Explanation:

Using the nth term formula:

`a_n=a_1+dn-d`

`a_7=3 \\ \\ n=7 \\ \\ d=-2`

`3=a_1+-2(7)-(-2)`

Simplifying and solving for the first term.

`3=a_1-14+2`

`3=a_1-12`

`15=a_1`

The first term of the sequence is 15.

Answer 2

`a_1=15`

Explanation:

We are talking about arithmetic progression.

Using the formula:

`a_n=a_1+(n-1) \cdot d`

`a_7=a_1+(7-1) \cdot d`

`3=a_1+(7-1) \cdot (-2)`

`3=a_1+(6) \cdot (-2)`

`3=a_1-12`

`a_1=15`