Advertisements
Advertisements
Question
Which term of the A.P. 3, 15, 27, 39, … will be 132 more than its 54th term?
Solution
a = 3, d = 15 - 3 = 12
Using Tn = a + (n - 1)d, we get
T54 = a + 53d
= 3 + 53 × 12
= 3 + 636
= 639
Let Tn be 132 more than its 54th term.
∴ Tn = T54 + 132
Tn = 639 + 132
Tn = 771
a + (n - l)d = 771
3 + (n - 1) × 12 = 771
(n - 1) × 12 = 771 - 3
(n - 1) × 12 = 768
(n - 1) = `768/12`
(n - 1) = 64
n = 64 + 1
n = 65
Thus, 132 more than 54th term is the 65th term.
APPEARS IN
RELATED QUESTIONS
Find the number of terms in the following A.P.: 7, 13, 19, ..., 205.
Subba Rao started work in 1995 at an annual salary of Rs 5000 and received an increment of Rs 200 each year. In which year did his income reach Rs 7000?
Find the sum of n terms of the series `(4 - 1/n) + (4 - 2/n) + (4 - 3/n)+ ......`
Write the first five terms of the following sequences whose nth term are:
`a_n = (n - 2)/3`
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 next five terms of the following sequences given by:
`a_1 = a_2 = 2, a_n = a_(n - 1) - 3, n > 2`
Which term of the A.P. 84, 80, 76, ... is 248?
Which term of the A.P. 21, 42, 63, 84, ... is 420?
The 4th term of an A.P. is three times the first and the 7th term exceeds twice the third term by 1. Find the first term and the common difference.
The sum of 4th and 8th terms of an A.P. is 24 and the sum of the 6th and 10th terms is 34. Find the first term and the common difference of the A.P.
Find:
the 9th term of the AP `3/4 , 5/4 , 7/4 , 9/4 ,.........`
Find the 37th term of the AP 6 , 7 `3/4 , 9 1/2 , 11 1/4,.............`
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 sum of first n terms of an AP is 3n2 + 4n. Find the 25th term of this AP ?
The 10th term from the end of the A.P. -5, -10, -15,…, -1000 is ______.
Write the first three terms of the APs when a and d are as given below:
a = –5, d = –3
Justify whether it is true to say that the following are the nth terms of an AP.
3n2 + 5
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 |
| -18 | ______ | 10 | 0 |
