Question

What is the 35th term of the arithmetic sequence where a1 = 13 and a17 = -67
A. -163
B. -160
C. -157
D. -154

Answer 1

\[a _{n} = a _{1} + (n - 1)d\]

Answer 2

\[a _{17} = 13 + 16d\]

Answer 3

\[-67 = 13 + 16d\]
\[-80 = 16d\]
d = -5

Answer 4

well, form equations to find out the common common difference. Let the first term 'a1' be simply 'a', and the common difference be 'd'.

As you may be knowing, the nth term of an AP is:
\[T_n= a + (n-1)d\]

Now,\[a_1 = a = 13\]
and\[a_{17} = a + (17 - 1)d = 13 + 16d = -67\]


From this find out 'd'. Then find out the 35th term using the formula for the nth term.

Answer 5

\[a _{35} = 13 + 34(-5) = -157\]

Answer 6

thank you:)

Answer 7

You're welcome :)