Finding Terms in Arithmetic Sequences Worksheet

Find the common difference d for the sequence: 4, 10, 16, 22, ...

d = 6 (calculated as 10 - 4)

Write the general term formula a_n for the sequence: 3, 8, 13, 18, ...

a_n = 3 + (n - 1)(5), which simplifies to a_n = 5n - 2

Find the 15th term of the sequence: 12, 9, 6, 3, ...

a_15 = -30 (a_1 = 12, d = -3; a_15 = 12 + 14(-3) = 12 - 42 = -30)

Find the 40th term of the sequence: -5, 1, 7, 13, ...

a_40 = 229 (a_1 = -5, d = 6; a_40 = -5 + 39(6) = -5 + 234 = 229)

A finite sequence is given by 8, 15, 22, ..., 141. How many terms are in this sequence?

20 terms (141 = 8 + (n - 1)(7) -> 133 = 7(n - 1) -> 19 = n - 1 -> n = 20)

The 4th term of an arithmetic sequence is 19 and the 9th term is 44. Find the first term a_1 and the common difference d.

d = 5 and a_1 = 4 (Since a_9 - a_4 = 5d, 44 - 19 = 25, so d = 5. Then 19 = a_1 + 3(5), giving a_1 = 4)