D. The sum of the 2nd and 7th terms of an A.P. is 30. If
its 15th term is 1 less than twice its 8th term, find the
AP.
Answers
Answer:
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Step-by-step explanation:
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Information provided with us:
- The sum of the 2nd and the 7th term of an A.P. is 30.
- 15th term is 1 less than twice its 8th term
What we have to calculate:
- A.P. (Arithmetic progression)
Performing Calculations:
We know that,
nth term of an A.P. is calculated by,
- t_n = a + (n - 1) d
Here,
- a is first term
- d is common difference
- n is no. of terms
2nd term:-
=> t_2 = a + (2 - 1) d
=> t_2 = a + (1) d
=> t_2 = a + d
7th term:-
=> t_7 = a + (7 - 1) d
=> t_7 = a + (6) d
=> t_7 = a + 6d
15th term:-
=> t_15 = a + (15 - 1) d
=> t_15 = a + (14) d
=> t_15 = a + 14d
8th term:-
=> t_8 = a + (8 - 1) d
=> t_8 = a + (7) d
=> t_8 = a + 7d
According to the question,
- 2nd term + 7th term = 30
=> a + d + a + 6d = 30
=> 2a + d + 6d = 30
=> 2a + 7d = 30
=> 2a = 30 - 7d -------------------------- [ Equation ]
Again according to the question,
a + 14d = 2 (a + 7d) - 1
=> a + 14d = 2 × (a + 7d) - 1
=> a + 14d = 2a + 14d - 1
=> 14d - 14d = 2a - a - 1
=> 2a - a - 1
=> a - 1
- Transposing the sides,
=> a = 1
Finding out common difference,
- Putting the value in equation,
=> 2(1) = 30 - 7d
=> 2 = 30 - 7d
=> 7d = 30 - 2
=> 7d = 28
=> d = 28 / 7
=> d = 4
Finding out A.P. :-
=> A.P. = 1, 5 , 9 , 13, 17 , ...
Hence,
- A.P. is 1, 5 , 9 , 13, 17 , ...