Two APs have the same first and last terms. The first AP has 21 terms with a common difference of 9. How many terms has the other AP if it's common difference is 4
Mathematics
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4 stepsLet 'a' be the first term and 'l' be the last term for both Arithmetic Progressions (APs).
The formula for the last term of an AP is:
l = a + (n - 1)d
where 'n' is the number of terms and 'd' is the common difference.
Write the expression for the last term of the first AP.
Given: n₁ = 21, d₁ = 9
l = a + (n₁ - 1)d₁
l = a + (21 - 1)9
l = a + (20)9
l = a + 180Write the expression for the last term of the second AP.
Given: d₂ = 4, n₂ = ?
l = a + (n₂ - 1)d₂
l = a + (n₂ - 1)4Equate the expressions for 'l' since the last terms are the same.
a + 180 = a + (n₂ - 1)4
Solve for n₂.
Subtract 'a' from both sides:
180 = (n₂ - 1)4
Divide both sides by 4:
180 / 4 = n₂ - 1
45 = n₂ - 1
Add 1 to both sides:
n₂ = 45 + 1
n₂ = 46The other AP has 46 terms.
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