Advertisements
Advertisements
Question
The sum of first 15 terms of an A.P. is 750 and its first term is 15. Find its 20th term.
Solution
Let a be the first term and d be the common difference.
Now, a = 15
Sum of first n terms of an AP is given by,
Sn = `"n"/(2)[2"a" + ("n" - 1)"d"]`
⇒ S15 = `(15)/(2)[2"a" + (15 - 1)"d"]`
⇒ 750 = `(15)/(2)(2"a" + 14"d")`
⇒ a + 7d = 50
⇒ 15 + 7d = 50
⇒ 7d = 35
⇒ d = 5
Now, 20th term = a20
= a + 19d
= 15 + 19 × 5
= 15 + 95
= 110.
RELATED QUESTIONS
Find the sum of all numbers from 50 to 350 which are divisible by 6. Hence find the 15th term of that A.P.
Find the sum of 20 terms of the A.P. 1, 4, 7, 10, ……
Find the sum of all natural numbers between 250 and 1000 which are exactly divisible by 3
Find the sum of first 22 terms of an AP in which d = 7 and 22nd term is 149.
Find the four numbers in A.P., whose sum is 50 and in which the greatest number is 4 times the least.
Find the sum to n term of the A.P. 5, 2, −1, −4, −7, ...,
In an A.P., the sum of first n terms is `(3n^2)/2 + 13/2 n`. Find its 25th term.
The sum of the first n terms of an AP in `((5n^2)/2 + (3n)/2)`.Find its nth term and the 20th term of this AP.
Write an A.P. whose first term is a and common difference is d in the following.
Write the expression of the common difference of an A.P. whose first term is a and nth term is b.
If `4/5` , a, 2 are three consecutive terms of an A.P., then find the value of a.
If \[\frac{1}{x + 2}, \frac{1}{x + 3}, \frac{1}{x + 5}\] are in A.P. Then, x =
Two A.P.'s have the same common difference. The first term of one of these is 8 and that of the other is 3. The difference between their 30th term is
The term A.P is 8, 10, 12, 14,...., 126 . find A.P.
Q.13
In a Arithmetic Progression (A.P.) the fourth and sixth terms are 8 and 14 respectively. Find that:
(i) first term
(ii) common difference
(iii) sum of the first 20 terms.
The sum of first 14 terms of an A.P. is 1050 and its 14th term is 140. Find the 20th term.
In an A.P. a = 2 and d = 3, then find S12
The first term of an AP is –5 and the last term is 45. If the sum of the terms of the AP is 120, then find the number of terms and the common difference.
The sum of 40 terms of the A.P. 7 + 10 + 13 + 16 + .......... is ______.
