the following A.P 2) 3,6,9,12,....
Answers
Answer:
Yes it is an AP with a = 3 and d = 3
mark me brainliest
Answer:
the given arithmetic progression or sequence: 3, 6, 9, 12, ... has a common difference of d = 3 because after the first term, which is 3, each term is 3 more than the one just before it.
Also, n will be a positive integer representing any given term in the sequence.
Now, in order to find the algebraic expression which will give us the nth term of the given sequence, we can analyze as follows:
First Term: 3 = 3(1)
Second Term: 6 = 3(2) = 3 + d = 3 + 3 = 3(1) + 3
Third Term: 9 = 3(3) = 6 + 3 = 3(2) + 3
Fourth Term: 12 = 4(3) = 9 + 3 = 3(3) + 3
Fifth Term: 15 = 5(3) = 12 + 3 = 3(4) + 3
Sixth Term: 18 = 6(3) = 15 + 3 = 3(5) + 3
Seventh Term: 21 = 7(3) = 18 + 3 = 3(6) + 3
Eighth Term: 24 = 8(3) = 21 + 3 = 3(7) + 3
.
.
.
(n - 2)th Term: (n - 2)(3) = 3(n - 3) + 3
(n - 1)th Term: (n - 1)(3) = 3(n - 2) + 3
nth Term: (n)(3) = 3n = 3(n - 1) + 3
= 3[(n - 1) + 1]
= 3[n - 1 + 1]
= 3[n + ((-1) + 1)]
= 3[n + 0]
= 3n
Therefore, the nth term of the given sequence is given by the algebraic expression: 3n.
CHECK:
The 1st term of the given sequence = 3n = 3(1) = 3
The 2nd term = 3n = 3(2) = 6
The 3rd term = 3n = 3(3) = 9
The 4th term = 3n = 3(4) = 12
The 5th term = 3n = 3(5) = 15
The 6th term = 3n = 3(6) = 18
The 7th term = 3n = 3(7) = 21
The 8th term = 3n = 3(8) = 24
.
.
.
The 30th term of the given sequence is 3(30) = 90 :
3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, 45, 48, 51, 54, 57, 60, 63, 66, 69, 72, 75, 78, 81, 84, 87, 90 (which is the 30th term).
please mark it as a brainliest answer and follow me