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.

Q1:

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 .

Q2:

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

Q3:

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

Q4:

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‘

Q5:

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

Q6:

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

Q7:

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

Q8:

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

Q9:

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

Q10:

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

Practice Means Progress

Download the Nagwa Practice app to access 100 additional questions for this lesson!

scan me!

Nagwa uses cookies to ensure you get the best experience on our website. Learn more about our Privacy Policy.