Question

Choose the correct equation for an arithmetic sequence in which t(4) = 8 and t(10) = 32 -

Answer 1

Answer:

The equation is $t(n) = -4 + 4(n-1)$

Step-by-step explanation:

Arithmetic sequence:

In an arithmetic sequence, the difference between consecutive terms, called common difference, is always the same.

The general equation for an arithmetic sequence is:

$t(n) = t(1) + d(n-1)$

Taking the mth term as reference, the equation can be written as:

$t(n) = t(m) + d(n-m)$

t(4) = 8 and t(10) = 32

The common difference can be found:

$t(n) = t(m) + d(n-m)$

$t(10) = t(4) + d(10-4)$

$6d = 24$

$d = \frac{24}{6} = 4$

So

$t(n) = t(1) + 4(n-1)$

Finding the first term:

$t(4) = t(1) + 4(n-1)$

So

$t(1) = t(4) - 12 = 8 - 12 = -4$

So

The equation is $t(n) = -4 + 4(n-1)$