Advertisements
Advertisements
प्रश्न
Find the sum of the following arithmetic progressions: 50, 46, 42, ... to 10 terms
Advertisements
उत्तर
In the given problem, we need to find the sum of terms for different arithmetic progressions. So, here we use the following formula for the sum of n terms of an A.P.,
`S_n =n/2 [2a + (n -1)d]`
Where a = first term for the given A.P.
d = common difference of the given A.P
n = number of terms
50, 46, 42, ... to 10 terms
Common difference of the A.P. (d)
`= a_2 - a_1`
= 46 - 50
= -4
Number of terms (n) = 10
First term for the given A.P. (a) = 50
So using the formula we get
`S_10 = 10/2 [2(50) + (10 - 1)(-4)]`
= (5)[100 + (9)(-4)]
= (5)[100 - 36]
= (5)[64]
= 320
Therefore the sum of first 10 terms for the given A.P is 320
APPEARS IN
संबंधित प्रश्न
Find the number of natural numbers between 101 and 999 which are divisible by both 2 and 5.
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.
If the sum of the first n terms of an A.P. is `1/2`(3n2 +7n), then find its nth term. Hence write its 20th term.
Find the sum given below:
–5 + (–8) + (–11) + ... + (–230)
Determine the A.P. Whose 3rd term is 16 and the 7th term exceeds the 5th term by 12.
Find the sum of first 12 natural numbers each of which is a multiple of 7.
Is -150 a term of the AP 11, 8, 5, 2, ……?
Which term of the A.P. `20, 19 1/4, 18 1/2, 17 3/4,` ..... is the first negative term?
A sum of ₹2800 is to be used to award four prizes. If each prize after the first is ₹200 less than the preceding prize, find the value of each of the prizes
Find the sum of the following Aps:
9, 7, 5, 3 … to 14 terms
If first term of an A.P. is a, second term is b and last term is c, then show that sum of all terms is \[\frac{\left( a + c \right) \left( b + c - 2a \right)}{2\left( b - a \right)}\].
Q.2
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.
In an A.P. (with usual notations) : given d = 5, S9 = 75, find a and a9
The sum of first 15 terms of an A.P. is 750 and its first term is 15. Find its 20th term.
How many terms of the A.P. 25, 22, 19, … are needed to give the sum 116 ? Also find the last term.
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`
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
If sum of first 6 terms of an AP is 36 and that of the first 16 terms is 256, find the sum of first 10 terms.
