Can someone me. this is an equation for either an arithmetic or geometric sequence.

A6 = -8
a15= -62

There are (15 - 6) terms in between, therefore 9 terms in between.
-8 to -62 ... there is a difference of 54
54 ÷ 9 = 6
Therefore it gets -6 each term.
a6 = -8, a7= -14, a8 = -20

That's an arithmetic sequence. To find the rule of the sequence, we need to find the first term (a₁) and the difference of the sequence (d)

Make an equation system based on what are given by the question.
an = a₁ + d(n - 1)

a₆ = a₁ + d(6 - 1) = -8
a₆ = a₁ + 5d = -8 (first equation)

a₁₅ = a₁ + d(15 - 1) = -62
a₁₅ = a₁ + 14d = -62 (second equation)

Solve the equation to find the value of a₁ and d
Using elimination method, find the value of d from first equation and second equation
a₁ + 14d = -62
a₁ +  5d =   -8
-   (substract)
        9d = -54
          d = -54/9
          d = -6

Using subtitution method, find the value of a₁. Subtitute d with -6 from the first equation.
a₁ + 5d = -8
a₁ + 5(-6) = -8
a₁ - 30 = -8
a₁ = -8 + 30
a₁ = 22

Determine the rule of the sequence
General rule for arithmetic sequence is
an = a + d(n - 1)

Now input the value of a₁ and d to the general rule, then simpllify.
an = a + d(n - 1)
an = 22 + -6(n - 1)
an = 22 -6n + 6
an = 28 - 6n

The rule of the sequence is 28 - 6n

38+105= 143, 39+104=143, and you will find then adding the numbers on opposite sides, moving inwards yields the answer 138 every time. because of this, you’re going to multiply 138 times the number of pairs, which is 34. therefore, 34*138= 4692(i’m sorry if it’s the wrong numbers, but it’s the right concept)