Example 1 · level 1
Find the 40th term of the AP −10, −7, −4, −1, …
Show solution
- a = −10, d = 3.
- a40 = −10 + (40 − 1) × 3 = −10 + 117
- = 107.
Answer: 107
CLASS 10 MATHS · ARITHMETIC PROGRESSIONS
Arithmetic progression: nth term
aₙ = a + (n − 1)d, where a is the first term and d the common difference.
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Worked examples
Example 2 · level 2
Which term of the AP 12, 8, 4, 0, … is −96?
Show solution
- 12 + (n − 1)(−4) = −96
- n − 1 = −108 ÷ (−4) = 27
- n = 28.
Answer: 28
Example 3 · level 3
In an AP, the 3th term is 16 and the 13th term is −14. Find the 38th term.
Show solution
- 10d = −14 − 16 = −30 → d = −3.
- a = 16 − 2 × (−3) = 22.
- a38 = 22 + 37 × (−3) = −89.
Answer: -89