4.2 Q-1 | Sequence And Series | Mathematics 11

Exercise 4.2 — Arithmetic Sequences: General Term

This exercise focuses on applying the general term formula for arithmetic sequences to find specific terms, common differences, and unknown values.

The $n^{t h}$ term of an arithmetic sequence is:

$a_{n} = a_{1} + (n - 1) d$

where:

A sequence is arithmetic if the difference between consecutive terms is constant:

$d = a_{2} - a_{1} = a_{3} - a_{2} = \dots = a_{n} - a_{n - 1}$

Example: Is $3, 7, 11, 15, \dots$ arithmetic?

Example 1: Find the 10th term of the sequence $2, 5, 8, 11, \dots$

$a_{1} = 2, d = 5 - 2 = 3, n = 10$ $a_{10} = 2 + (10 - 1) (3) = 2 + 27 = 29$

Example 2: Find the common difference if $a_{1} = 4$ and $a_{7} = 22$ .

$a_{7} = a_{1} + 6 d ⟹ 22 = 4 + 6 d ⟹ d = 3$

Example 3: Which term of the sequence $1, 4, 7, 10, \dots$ equals $31$ ?

$31 = 1 + (n - 1) (3) ⟹ 30 = 3 (n - 1) ⟹ n = 11$