The 5th term of an arithmetic sequence is 34and the 9 th term is 65 what is the first term
Answers
Answer:
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Answer:
Let a be the first term of the Arithmetic progression, d be the Arithmetic progression.
common difference of the
5th term= a + 4d
9th term= a + 8d.
According to the question,
The sum of 5th and 9th terms of AP is 40.
So, ( + 4d)+( a + 8d) = 40
2a + 12 d = 40
a + 6d = 20
8th term = a + 7d
14th term= a + 13d
According to the question,
The sum of 8th and 14th terms of AP is 64
So, a + 7d + a + 13 d = 64
2a + 20 d = 64
a + 10d = 32
We have two equations in two variables, We shall now solve them.
a + 10d = 32
a + 6d = 20
We get, 4d = 12, d = 3 on subtracting both the equations.
Now, a = 20 - 6d = 20 - 6(3) = 2
Sum of n terms of an A.P is defined,
Sn = (2a + (n-1)d)
We need sum of first 20 terms, so n = 20
S20 20 2 = (2 × 2 + (201) × 3)
=
10(4 + 19 × 3)
= 10(4+57) = 10 x 61 610 =
Therefore, The sum of first 20 terms is 610