Advertisements
Advertisements
Question
The sum of the first three terms of an A.P. is 33. If the product of the first and the third terms exceeds the second term by 29, find the A.P.
Solution
Let first three terms of A.P. be a – d, a, a + d.
Given, a – d + a + a + d = 33
⇒ 3a = 33
⇒ a = 11 ...(i)
And (a – d)(a + d) = a + 29
⇒ a2 – d2 = a + 29
⇒ (11)2 – d2 = 11 + 29 ...[From equation (i)]
⇒ 121 – d2 = 40
⇒ d2 = 81
⇒ d = ± 9
When, a = 11 and d = 9
Then, A.P. is 2, 11, 20......
When, a = 11 and d = –9
Then, A.P. is 20, 11, 2......
APPEARS IN
RELATED QUESTIONS
Find the sum of n terms of the series `(4 - 1/n) + (4 - 2/n) + (4 - 3/n)+ ......`
Find the indicated terms in the following sequences whose nth terms are:
an = 5n - 4; a12 and a15
Find the next five terms of the following sequences given by
a1 = a2 = 2, an = an−1 − 3, n > 2
Find the nth term of the following Aps:
(i) 5, 11, 17, 23 …
The 17th term of AP is 5 more than twice its 8th term. If the 11th term of the AP is 43, find its nth term.
Reshma wanted to save at least Rs 6,500 for sending her daughter to school next year (after 12 month.) She saved Rs 450 in the first month and raised her savings by Rs 20 every next month. How much will she be able to save in next 12 months? Will she be able to send her daughter to the school next year?
What value is reflected in this question ?
The next term of the AP `sqrt18, sqrt50, sqrt98, ....` is ______.
Justify whether it is true to say that the following are the nth terms of an AP.
2n – 3
Find the 20th term of the AP whose 7th term is 24 less than the 11th term, first term being 12.
Fill in the blank in the following table, given that a is the first term, d the common difference, and an nth term of the AP:
| a | d | n | an |
| 3.5 | 0 | 105 | ______ |
