The common difference of two different AP's is equal. The first term of the first AP is 3 more than the first term of second AP. If the 7th term of the first AP is 28 and 8th term of second AP is 29, and then find the APS
Answers
Answer:
tq
Step-by-step explanation:
Each year, the AP Program develops and administers multiple versions of the AP Exam for each AP subject. Each version is developed with the same format, number, and type of questions.
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Answer:
First AP: 4, 8, 12, 16. . . . .
Second AP: 1, 5, 9, 13. . . . .
Step-by-step explanation:
Given that:
The common difference of two AP are equal.
To Find:
Both the AP.
We know that:
aₙ = a + (n - 1)d
Where,
aₙ = nth term
a = First term
n = Number of terms
d = Common difference
Let us assume:
Common difference be d.
First term of first AP be a.
First term of second AP be A.
The 1st term of an AP is 3 more than the 1st term of second AP:
⇢ a = A + 3 _____(i)
The 7th term of AP is 28:
⇢ a₇ = 28
⇢ a + (7 - 1)d = 28
⇢ a + 6d = 28
Substituting the value of a from eqⁿ(i).
⇢ A + 3 + 6d = 28
⇢ A = 28 - 3 - 6d
⇢ A = 25 - 6d _____(ii)
8th term of second AP is 29:
⇢ A₈ = 29
⇢ A + (8 - 1)d = 29
⇢ A + 7d = 29
Substituting the value of A from eqⁿ(ii).
⇢ 25 - 6d + 7d = 29
⇢ 25 + d = 29
⇢ d = 29 - 25
⇢ d = 4
In equation (ii).
⇢ A = 25 - 6d
Putting the value of d.
⇢ A = 25 - 6(4)
⇢ A = 25 - 24
⇢ A = 1
In equation (i)
⇢ a = A + 3
Putting the value of A.
⇢ a = 1 + 3
⇢ a = 4
Finding first AP:
Common difference = d = 4
First term of first AP = a = 4
Second term = a + d = 4 + 4 = 8
Third term = a + 2d = 4 + 2(4) = 12
Fourth term = a + 3d = 4 + 3(4) = 16
∴ First AP: 4, 8, 12, 16. . . . .
Finding second AP:
Common difference = d = 4
First term of second AP = 1
Second term = a + d = 1 + 4 = 5
Third term = a + 2d = 1 + 2(4) = 9
Fourth term = a + 3d = 1 + 3(4) = 13
∴ Second AP: 1, 5, 9, 13. . . . .