Question 1

An arithmetic sequence has first term $a = 4$ and common difference $d = 3$. What is $T_5$?

Accepted Answer

16 — $T_5 = a + 4d = 4 + 4(3) = 4 + 12 = 16$.

Question 2

A sequence is $5; 9; 13; 17; \ldots$ What is the common difference $d$?

Accepted Answer

4 — $d = T_2 - T_1 = 9 - 5 = 4$ (check: $13 - 9 = 4$ also).

Question 3

For the sequence $5; 9; 13; 17; \ldots$, find $T_{10}$ using $T_n = a + (n-1)d$ with $a=5$, $d=4$.

Accepted Answer

41 — $T_{10} = 5 + (10-1)(4) = 5 + 36 = 41$.

Patterns, Sequences & Series

Sample practice questions