Lesson Worksheet: Using Arithmetic Sequence Formulas Mathematics • 9th Grade

In this worksheet, we will practice writing explicit and recursive formulas for arithmetic sequences to find the value of the 𝑛th term in an arithmetic sequence and finding a term’s order given its value.


Fill in the blank: If the first term of an arithmetic sequence equals 16 and ๐‘Ž=๐‘Ž+2๏Š๏Šฐ๏Šง๏Š, then the fifth term equals .


Find, in terms of ๐‘›, the general term of the arithmetic sequence โˆ’7,โˆ’5,โˆ’3,โˆ’1,โ€ฆ.

  • A๐‘Ž=โˆ’7๐‘›+2๏Š
  • B๐‘Ž=2๐‘›โˆ’9๏Š
  • C๐‘Ž=2๐‘›๏Š
  • D๐‘Ž=โˆ’7๐‘›โˆ’9๏Š
  • E๐‘Ž=โˆ’9๐‘›+2๏Š


Using the table, determine the expression that represents the value of each term as a function of its position. Then, find the value of the eighteenth term in the sequence.

Position 6 7 8 9 ๐‘›
Value of Term 19 22 25 28 โ‹ฏ
  • A๐‘›, 22
  • B3๐‘›, 54
  • C๐‘›+1, 24
  • D3๐‘›+1, 55
  • E3๐‘›โˆ’1, 53


Find ๐‘Ž๏Šง๏Šฏ in the arithmetic sequence (12๐‘Ž+9๐‘,16๐‘Ž+13๐‘,20๐‘Ž+17๐‘,โ€ฆ).

  • A84๐‘Ž+89๐‘
  • B84๐‘Ž+81๐‘
  • C92๐‘Ž+89๐‘
  • D88๐‘Ž+85๐‘


Find the general term of the arithmetic sequence which satisfies the relations ๐‘Ž+๐‘Ž=โˆ’30๏Šฌ๏Šฎ and ๐‘Žร—๐‘Ž=525๏Šญ๏Šฏ.

  • A๐‘Ž=โˆ’10๐‘›+35๏Š
  • B๐‘Ž=5552๐‘›โˆ’570๏Š
  • C๐‘Ž=โˆ’10๐‘›โˆ’25๏Š
  • D๐‘Ž=โˆ’10๐‘›+45๏Š
  • E๐‘Ž=โˆ’10๐‘›+55๏Š


Find the number of terms in the arithmetic sequence (โˆ’4,2,8,โ€ฆ,392).


Find the order of the term whose value is 112 in the sequence (17,22,27,32,โ€ฆ).

  • A๐‘Ž๏Šจ๏Šฆ
  • B๐‘Ž๏Šจ๏Šง
  • C๐‘Ž๏Šง๏Šฏ
  • D๐‘Ž๏Šง๏Šฎ


Find the first three terms in the sequence which has general term ๐‘Ž=17+14๐‘›๏Š and ๐‘›โ‰ฅ1. Then find the order of the term whose value is 157 and the order of the first term whose value is more than 100.

  • A45,59,73, ๐‘Ž๏Šง๏Šฆ, ๐‘Ž๏Šฌ
  • B31,45,59, ๐‘Ž๏Šง๏Šฆ, ๐‘Ž๏Šฌ
  • C45,59,73, ๐‘Ž๏Šง๏Šง, ๐‘Ž๏Šซ
  • D31,45,59, ๐‘Ž๏Šฏ, ๐‘Ž๏Šซ


Find the ๐‘›th term of the arithmetic sequence given that ๐‘Žโˆ’๐‘Ž=26๏Šฉ๏Šซ and ๐‘Ž=44๏Šช. Then find the position and value of the first negative term in the sequence.

  • A83โˆ’13๐‘›, 7, 5
  • B109โˆ’13๐‘›, 7, โˆ’8
  • C96โˆ’13๐‘›, 8, โˆ’8
  • D83โˆ’13๐‘›, 8, 5


Find ๐‘ฅ and the number of terms in the arithmetic sequence 4โˆ’18๐‘ฅ,โˆ’30๐‘ฅโˆ’7,โ€ฆ,โˆ’22๐‘ฅ+17,โˆ’29๐‘ฅ+11.

  • Aโˆ’1,18
  • Bโˆ’1,19
  • C1,18
  • D1,19

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