Advertisements
Advertisements
Question
Find the sum of first 22 terms of an AP in which d = 7 and 22nd term is 149.
Advertisements
Solution
d = 7
a22 = 149
S22 = ?
an = a + (n − 1)d
a22 = a + (22 − 1)d
149 = a + 21 × 7
149 = a + 147
a = 2
`S_n = n/2(a+a_n)`
= `22/2(2+149)`
= 11(151)
= 1661
RELATED QUESTIONS
How many terms of the series 54, 51, 48, …. be taken so that their sum is 513 ? Explain the double answer
The ratio of the sums of m and n terms of an A.P. is m2 : n2. Show that the ratio of the mth and nth terms is (2m – 1) : (2n – 1)
Find the sum of the following APs.
−37, −33, −29, …, to 12 terms.
Find the sum given below:
34 + 32 + 30 + ... + 10
How many terms of the AP. 9, 17, 25 … must be taken to give a sum of 636?
Find the sum of the following arithmetic progressions
`(x - y)^2,(x^2 + y^2), (x + y)^2,.... to n term`
Show that the sum of all odd integers between 1 and 1000 which are divisible by 3 is 83667.
If numbers n – 2, 4n – 1 and 5n + 2 are in A.P., find the value of n and its next two terms.
The sum of first three terms of an AP is 48. If the product of first and second terms exceeds 4 times the third term by 12. Find the AP.
Find the sum of first n even natural numbers.
The sum of the first n terms of an AP is (3n2+6n) . Find the nth term and the 15th term of this AP.
In an A.P. 17th term is 7 more than its 10th term. Find the common difference.
Choose the correct alternative answer for the following question.
For an given A.P. a = 3.5, d = 0, n = 101, then tn = ....
The Sum of first five multiples of 3 is ______.
If the common differences of an A.P. is 3, then a20 − a15 is
The first and last terms of an A.P. are 1 and 11. If the sum of its terms is 36, then the number of terms will be
If the sum of three consecutive terms of an increasing A.P. is 51 and the product of the first and third of these terms is 273, then the third term is
Two cars start together in the same direction from the same place. The first car goes at uniform speed of 10 km h–1. The second car goes at a speed of 8 km h–1 in the first hour and thereafter increasing the speed by 0.5 km h–1 each succeeding hour. After how many hours will the two cars meet?
Q.3
Q.4
The sum of first 14 terms of an A.P. is 1050 and its 14th term is 140. Find the 20th term.
The sum of the first three numbers in an Arithmetic Progression is 18. If the product of the first and the third term is 5 times the common difference, find the three numbers.
How many terms of the A.P. 25, 22, 19, … are needed to give the sum 116 ? Also find the last term.
In an A.P. a = 2 and d = 3, then find S12
Find the sum of those integers from 1 to 500 which are multiples of 2 or 5.
[Hint (iii) : These numbers will be : multiples of 2 + multiples of 5 – multiples of 2 as well as of 5]
Find the sum:
`(a - b)/(a + b) + (3a - 2b)/(a + b) + (5a - 3b)/(a + b) +` ... to 11 terms
Find the sum of first 17 terms of an AP whose 4th and 9th terms are –15 and –30 respectively.
Find the sum of all the 11 terms of an A.P. whose middle most term is 30.
The sum of all two digit numbers is ______.
The nth term of an A.P. is 6n + 4. The sum of its first 2 terms is ______.
