Advertisements
Advertisements
Question
Fill up the boxes and find out the number of terms in the A.P.
1,3,5,....,149 .
Here a = 1 , d =b`[ ], t_n = 149`
tn = a + (n-1) d
∴ 149 =`[ ] ∴149 = 2n - [ ]`
∴ n =`[ ]`
Advertisements
Solution
In the A.P. 1,3,5,....,149
a = 1 , d = 2 , tn = 149
tn = a + (n-1)d
149 = 1+ (n-1) × 2
149 = 1 + 2n -2
149 = 2n - 1
∴ 2n = 150
∴ n = 75
APPEARS IN
RELATED QUESTIONS
The houses in a row numbered consecutively from 1 to 49. Show that there exists a value of x such that sum of numbers of houses preceding the house numbered x is equal to sum of the numbers of houses following x.
Check whether -150 is a term of the A.P. 11, 8, 5, 2, ....
How many terms of the AP. 9, 17, 25 … must be taken to give a sum of 636?
Find the sum of the first 25 terms of an A.P. whose nth term is given by an = 7 − 3n
Find the sum of all integers between 100 and 550, which are divisible by 9.
Find the sum of all 3 - digit natural numbers which are divisible by 13.
Determine the A.P. Whose 3rd term is 16 and the 7th term exceeds the 5th term by 12.
Find the sum of the first 22 terms of the A.P. : 8, 3, –2, ………
The first term of an A.P. is 5, the last term is 45 and the sum of its terms is 1000. Find the number of terms and the common difference of the A.P.
The 8th term of an AP is zero. Prove that its 38th term is triple its 18th term.
The sum of the first n terms in an AP is `( (3"n"^2)/2 +(5"n")/2)`. Find the nth term and the 25th term.
Find the sum of all multiples of 9 lying between 300 and 700.
There are 25 trees at equal distances of 5 metres in a line with a well, the distance of the well from the nearest tree being 10 metres. A gardener waters all the trees separately starting from the well and he returns to the well after watering each tree to get water for the next. Find the total distance the gardener will cover in order to water all the trees.
Write the sum of first n odd natural numbers.
The first and last term of an A.P. are a and l respectively. If S is the sum of all the terms of the A.P. and the common difference is given by \[\frac{l^2 - a^2}{k - (l + a)}\] , then k =
If in an A.P. Sn = n2p and Sm = m2p, where Sr denotes the sum of r terms of the A.P., then Sp is equal to
Sum of n terms of the series `sqrt2+sqrt8+sqrt18+sqrt32+....` is ______.
Q.13
The sum of first ten natural number is ______.
Find the sum:
`(a - b)/(a + b) + (3a - 2b)/(a + b) + (5a - 3b)/(a + b) +` ... to 11 terms
