) If a₁ = 37 and a21 = -3 then + what is d? an = a₁ + (n-1) d
Answer (1)
The common difference is -2 and this is arithmetic sequenceTo solve for d, first write down the formula. [tex] a_{n} = a_{1} + (n - 1)d[/tex]List down the given values, we have:[tex] a_{n} = - 3[/tex][tex]a_{1} = 37[/tex][tex]n = 21[/tex]*n is equal to 21, since there is no given n, we can simply note 21 as n. Also, if we observe the given values, it seems like this is an example of a finite sequence.*Next, substitute the given values to the formula and we can now solve it. Subtract 37 from both sides. Divide 20 from both sides, resulting to -2. [tex]a_{n} = a_{1} + (n - 1)d \\ - 3 = 37 + (21 - 1)d \\ - 3 = 37 + 20d \\ - 3 - 37 = { \cancel{37 - 37}} + 20d \\ - 3 - 37= 20d \\ - 40 = 20d \\ \frac{ - 40}{20} = \frac{{ \cancel{20}}d}{{ \cancel{20}}} \\ \frac{ - 40}{20} = d \\ - 2 = d[/tex]The common difference is -2
