Advertisements
Advertisements
Question
Find the sum of the following APs:
2, 7, 12, ..., to 10 terms.
Advertisements
Solution
2, 7, 12, …, to 10 terms
For this A.P.,
a = 2
d = a2 − a1
d = 7 − 2
d = 5
n = 10
We know that,
Sn = `n/2 [2a + (n - 1) d]`
S10 = `10/2 [2(2) + (10 - 1) × 5]`
= 5[4 + (9) × (5)]
= 5 × 49
= 245
Thus, the sum of first 10 terms is 245.
RELATED QUESTIONS
If the sum of first 7 terms of an A.P. is 49 and that of its first 17 terms is 289, find the sum of first n terms of the A.P.
How many terms of the A.P. 65, 60, 55, .... be taken so that their sum is zero?
Divide 32 into four parts which are in A.P. such that the product of extremes is to the product of means is 7 : 15.
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`
In an AP: Given a = 5, d = 3, an = 50, find n and Sn.
Show that a1, a2,..., an... form an AP where an is defined as below:
an = 9 − 5n
Also, find the sum of the first 15 terms.
Find the sum of all integers between 100 and 550, which are divisible by 9.
Find the sum of the first 11 terms of the A.P : 2, 6, 10, 14, ...
How many terms of the A.P. : 24, 21, 18, ................ must be taken so that their sum is 78?
Find the sum of all odd natural numbers less than 50.
What is the sum of first n terms of the AP a, 3a, 5a, …..
Which term of the AP 21, 18, 15, … is zero?
Find the sum of first n even natural numbers.
How many terms of the A.P. 21, 18, 15, … must be added to get the sum 0?
Find the sum of all multiples of 9 lying between 300 and 700.
Kargil’s temperature was recorded in a week from Monday to Saturday. All readings were in A.P. The sum of temperatures of Monday and Saturday was 5°C more than sum of temperatures of Tuesday and Saturday. If temperature of Wednesday was –30° celsius then find the temperature on the other five days.
The A.P. in which 4th term is –15 and 9th term is –30. Find the sum of the first 10 numbers.
There are 37 terms in an A.P., the sum of three terms placed exactly at the middle is 225 and the sum of last three terms is 429. Write the A.P.
If Sn denotes the sum of the first n terms of an A.P., prove that S30 = 3(S20 − S10)
Write the expression of the common difference of an A.P. whose first term is a and nth term is b.
If \[\frac{5 + 9 + 13 + . . . \text{ to n terms} }{7 + 9 + 11 + . . . \text{ to (n + 1) terms}} = \frac{17}{16},\] then n =
The first three terms of an A.P. respectively are 3y − 1, 3y + 5 and 5y + 1. Then, y equals
Q.13
Q.14
If the second term and the fourth term of an A.P. are 12 and 20 respectively, then find the sum of first 25 terms:
The 11th term and the 21st term of an A.P are 16 and 29 respectively, then find the first term, common difference and the 34th term.
A merchant borrows ₹ 1000 and agrees to repay its interest ₹ 140 with principal in 12 monthly instalments. Each instalment being less than the preceding one by ₹ 10. Find the amount of the first instalment.
The famous mathematician associated with finding the sum of the first 100 natural numbers is ______.
The sum of the first five terms of an AP and the sum of the first seven terms of the same AP is 167. If the sum of the first ten terms of this AP is 235, find the sum of its first twenty terms.
Read the following passage:
|
India is competitive manufacturing location due to the low cost of manpower and strong technical and engineering capabilities contributing to higher quality production runs. The production of TV sets in a factory increases uniformly by a fixed number every year. It produced 16000 sets in 6th year and 22600 in 9th year. |
- In which year, the production is 29,200 sets?
- Find the production in the 8th year.
OR
Find the production in first 3 years. - Find the difference of the production in 7th year and 4th year.
