Advertisements
Advertisements
प्रश्न
In an A.P. sum of three consecutive terms is 27 and their products is 504. Find the terms. (Assume that three consecutive terms in an A.P. are a – d, a, a + d.)
Advertisements
उत्तर
Let the three consecutive terms in an A.P. be a – d, a, and a + d.
According to the first condition,
sum of three consecutive terms is 27.
a – d + a + a + d = 27
∴ 3a = 27
∴ a = `27/3`
∴ a = 9 ..........(i)
According to the second condition,
the product of the three numbers is 504.
(a – d) a (a + d) = 504
∴ a(a2 – d2) = 504
∴ 9(92 – d2) = 504 ........[From(i)]
∴ 81 – d2 = `504/9`
∴ 81 – d2 = 56
∴ d2 = 81 – 56
∴ d2 = 25
Taking square root of both sides, we get
d = ±5
When d = 5 and a = 9,
a – d = 9 – 5 = 4
a = 9
a + d = 9 + 5 = 14
When d = – 5 and a = 9,
a – d = 9 – (– 5) = 9 + 5 = 14
a = 9
a + d = 9 – 5 = 4
∴ The three consecutive terms are 4, 9 and 14 or 14, 9 and 4.
APPEARS IN
संबंधित प्रश्न
Find four numbers in A.P. whose sum is 20 and the sum of whose squares is 120
In an AP: Given a = 5, d = 3, an = 50, find n and Sn.
Determine the nth term of the AP whose 7th term is –1 and 16th term is 17.
If the numbers (2n – 1), (3n + 2) and (6n – 1) are in AP, find the value of n and the numbers.
How many terms of the AP 63, 60, 57, 54, ... must be taken so that their sum is 693? Explain the double answer.
In an A.P. 19th term is 52 and 38th term is 128, find sum of first 56 terms.
In an A.P. sum of three consecutive terms is 27 and their product is 504, find the terms.
(Assume that three consecutive terms in A.P. are a – d, a, a + d).
Rs 1000 is invested at 10 percent simple interest. Check at the end of every year if the total interest amount is in A.P. If this is an A.P. then find interest amount after 20 years. For this complete the following activity.
Find the sum:
\[18 + 15\frac{1}{2} + 13 + ... + \left( - 49\frac{1}{2} \right)\]
A man is employed to count Rs 10710. He counts at the rate of Rs 180 per minute for half an hour. After this he counts at the rate of Rs 3 less every minute than the preceding minute. Find the time taken by him to count the entire amount.
If the sum of n terms of an A.P. is 3n2 + 5n then which of its terms is 164?
The number of terms of the A.P. 3, 7, 11, 15, ... to be taken so that the sum is 406 is
Q.3
The sum of the first three numbers in an Arithmetic Progression is 18. If the product of the first and the third term is 5 times the common difference, find the three numbers.
In an A.P. (with usual notations) : given d = 5, S9 = 75, find a and a9
The sum of first 15 terms of an A.P. is 750 and its first term is 15. Find its 20th term.
Find the sum of first 1000 positive integers.
Activity :- Let 1 + 2 + 3 + ........ + 1000
Using formula for the sum of first n terms of an A.P.,
Sn = `square`
S1000 = `square/2 (1 + 1000)`
= 500 × 1001
= `square`
Therefore, Sum of the first 1000 positive integer is `square`
Show that the sum of an AP whose first term is a, the second term b and the last term c, is equal to `((a + c)(b + c - 2a))/(2(b - a))`
Find the middle term of the AP. 95, 86, 77, ........, – 247.
Sum of 1 to n natural number is 45, then find the value of n.
