Advertisements
Advertisements
प्रश्न
Find the 20th term from the last term of the A.P. 3, 8, 13, …, 253.
Advertisements
उत्तर
Given A.P. is
3, 8, 13, …, 253
Common difference for this A.P. is 5.
Therefore, this A.P. can be written in reverse order as
253, 248, 243, …, 13, 8, 3
For this A.P.,
a = 253
d = 248 − 253
d = −5
n = 20
a20 = a + (20 − 1) d
a20 = 253 + (19) (−5)
a20 = 253 − 95
a = 158
Therefore, 20th term from the last term is 158.
APPEARS IN
संबंधित प्रश्न
How many terms of the A.P. 27, 24, 21, .... should be taken so that their sum is zero?
The sum of the first p, q, r terms of an A.P. are a, b, c respectively. Show that `\frac { a }{ p } (q – r) + \frac { b }{ q } (r – p) + \frac { c }{ r } (p – q) = 0`
How many multiples of 4 lie between 10 and 250?
Find the sum of the odd numbers between 0 and 50.
In a potato race, a bucket is placed at the starting point, which is 5 m from the first potato and other potatoes are placed 3 m apart in a straight line. There are ten potatoes in the line.
A competitor starts from the bucket, picks up the nearest potato, runs back with it, drops it in the bucket, runs back to pick up the next potato, runs to the bucket to drop it in, and she continues in the same way until all the potatoes are in the bucket. What is the total distance the competitor has to run?
[Hint: to pick up the first potato and the second potato, the total distance (in metres) run by a competitor is 2 × 5 + 2 ×(5 + 3)]
If the pth term of an A. P. is `1/q` and qth term is `1/p`, prove that the sum of first pq terms of the A. P. is `((pq+1)/2)`.
How many terms are there in the A.P. whose first and fifth terms are −14 and 2 respectively and the sum of the terms is 40?
Find the sum of the first 51 terms of the A.P: whose second term is 2 and the fourth term is 8.
In an A.P., the sum of first n terms is `(3n^2)/2 + 13/2 n`. Find its 25th term.
Find the sum of 28 terms of an A.P. whose nth term is 8n – 5.
Find the middle term of the AP 10, 7, 4, ……., (-62).
The 19th term of an AP is equal to 3 times its 6th term. If its 9th term is 19, find the AP.
If the sum of first m terms of an AP is ( 2m2 + 3m) then what is its second term?
Find the sum of first n terms of an AP whose nth term is (5 - 6n). Hence, find the sum of its first 20 terms.
Find the first term and common difference for the A.P.
0.6, 0.9, 1.2,1.5,...
In an A.P. 19th term is 52 and 38th term is 128, find sum of first 56 terms.
Choose the correct alternative answer for the following question .
If for any A.P. d = 5 then t18 – t13 = ....
Choose the correct alternative answer for the following question .
In an A.P. 1st term is 1 and the last term is 20. The sum of all terms is = 399 then n = ....
Write the common difference of an A.P. whose nth term is an = 3n + 7.
Write the value of x for which 2x, x + 10 and 3x + 2 are in A.P.
Sum of n terms of the series `sqrt2+sqrt8+sqrt18+sqrt32+....` is ______.
The 9th term of an A.P. is 449 and 449th term is 9. The term which is equal to zero is
If the sums of n terms of two arithmetic progressions are in the ratio \[\frac{3n + 5}{5n - 7}\] , then their nth terms are in the ratio
If 18, a, b, −3 are in A.P., the a + b =
If k, 2k − 1 and 2k + 1 are three consecutive terms of an A.P., the value of k is
Q.6
Determine the sum of first 100 terms of given A.P. 12, 14, 16, 18, 20, ......
Activity :- Here, a = 12, d = `square`, n = 100, S100 = ?
Sn = `"n"/2 [square + ("n" - 1)"d"]`
S100 = `square/2 [24 + (100 - 1)"d"]`
= `50(24 + square)`
= `square`
= `square`
An AP consists of 37 terms. The sum of the three middle most terms is 225 and the sum of the last three is 429. Find the AP.
Find the sum:
1 + (–2) + (–5) + (–8) + ... + (–236)
Kanika was given her pocket money on Jan 1st, 2008. She puts Rs 1 on Day 1, Rs 2 on Day 2, Rs 3 on Day 3, and continued doing so till the end of the month, from this money into her piggy bank. She also spent Rs 204 of her pocket money, and found that at the end of the month she still had Rs 100 with her. How much was her pocket money for the month?
