Question

In an arithmetic​ sequence, the nth term an is given by the formula An=a1+(n−1)d​, where a1is the first term and d is the common difference.​ Similarly, in a geometric​ sequence, the nth term is given by an=a1•rn−1.

Use these formulas to determine the indicated term in the given sequence.

The 19th term of 19​,42​,65​,88​,...

Answer 1

Answer: 433

Explanation:

The given sequence : 19​,42​,65​,88​,...

We can see that the terms ha common difference as :-

`42-19=23\\65-42=23\\88-65=23`

Thus, its an Arithmetic progression with common difference (d)=23

The formula to find the nth term is :-

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

Now, the 19th term of the given sequence :-

`a_(19)=19+(19-1)(23)\\\\=19+(18)(23)\\\\=19+414=433`

Hence, the 19th term of 19​,42​,65​,88​,... is 433.