5n+2 is the
is the general form of an
arthematic
sequence
find
common difference ?
the first term and 20th
term
Answers
Answer- The above question is from the chapter 'Arithmetic Progressions'.
Concept used: 1) Common difference (d) = a₂ - a₁
2) aₙ = a + (n - 1)d
where aₙ = nth term or last term of an AP
a = first term of AP
n = Number of terms of AP
d = Common difference
Given question: 5n + 2 is the general form of an arithmetic sequence.
Find the common difference, the first term and 20th term.
Solution: General form of an AP = 5n + 2
Put n = 1, a₁ = 5 (1) + 2 = 5 + 2 = 7
Put n = 2, a₂ = 5 (2) + 2 = 10 + 2 = 12
Put n = 3, a₃ = 5 (3) + 2 = 15 + 2 = 17
⇒ A.P. = 5, 12, 17, _ _ _, 5n + 2
whose first term (a) = 7
common difference (d) = 12 - 7 = 5
20th term = a + (20 - 1)d = 7 + 19(5) = 102
∴ Common difference = 5
First term = 7
Twentieth term = 102
Answer:
Answer- The above question is from the chapter 'Arithmetic Progressions'.
Concept used: 1) Common difference (d) = a₂ - a₁
2) aₙ = a + (n - 1)d
where aₙ = nth term or last term of an AP
a = first term of AP
n = Number of terms of AP
d = Common difference
Given question: 5n + 2 is the general form of an arithmetic sequence.
Find the common difference, the first term and 20th term.
Solution: General form of an AP = 5n + 2
Put n = 1, a₁ = 5 (1) + 2 = 5 + 2 = 7
Put n = 2, a₂ = 5 (2) + 2 = 10 + 2 = 12
Put n = 3, a₃ = 5 (3) + 2 = 15 + 2 = 17
⇒ A.P. = 5, 12, 17, _ _ _, 5n + 2
whose first term (a) = 7
common difference (d) = 12 - 7 = 5
20th term = a + (20 - 1)d = 7 + 19(5) = 102
∴ Common difference = 5
First term = 7
Twentieth term = 102