Advertisements
Advertisements
Question
The sum of three consecutive terms that are in A.P. is 27 and their product is 288. Find the three terms
Solution
Let the three consecutive terms be a – d, a and a + d
By the given first condition
a – d + a + a + d = 27
3a = 27
a = `27/3` = 9
Again by the second condition
(a – d) (a) (a + d) = 288
a(a2 – d2) = 288
9(81 – d2) = 288 (a = 9)
81 – d2 = `288/9`
81 – d2 = 32
∴ d2 = 81 – 32
= 49
d = `sqrt(49)` = ± 7
When a = 9, d = 7
a + d = 9 + 7 = 16
a = 9
a – d = 9 – 7 = 2
When a = 9, d = – 7
a + d = 9 – 7 = 2
a = 9
a – d = 9 – (–7) = 9 + 7 = 16
The three terms are 2, 9, 16 (or) 16, 9, 2
APPEARS IN
RELATED QUESTIONS
In an AP of 50 terms, the sum of first 10 terms is 210 and the sum of its last 15 terms is 2565. Find the A.P.
Determine the general term of an A.P. whose 7th term is –1 and 16th term 17
Following are APs or not? If they form an A.P. find the common difference d and write three more terms:
1, 3, 9, 27 …
Following are APs or not? If they form an A.P. find the common difference d and write three more terms:
`sqrt2, sqrt8, sqrt18, sqrt32 ...`
Write the arithmetic progressions write the first term a and common difference d is as follows:
a = 4,d = -3
Write the arithmetic progressions write the first term a and common difference d is as follows:
a = -1.5, d = -0.5
Find the middle term of the A.P. 213, 205, 197, ...., 37.
Which term of an A.P. 16, 11, 6, 1, ... is – 54?
Find x, y and z, given that the numbers x, 10, y, 24, z are in A.P.
Split 207 into three parts such that these are in AP and the product of the two smaller parts is 4623.
