The number of terms of the A.P. 26, 22, 18, 14, ... that must be taken for the sum to be - 64 is
Answers
Answer:
n=2
Step-by-step explanation:
-64=n/2[2a+(n-1)d]
-64=n/2[52+(n-1)-4]
-128=n[56-4n]
-32=n[14-n]
-32=14n-n^2
n^2-14n-32=0
n^2-2n+16n-32=0
n=-16,n=2
no. of terms will be +ve thus n=2
mark as Brainliest plz
Given : A.P. 26, 22, 18, 14, ...
To Find : The number of terms of the A.P. must be taken for the sum to be - 64
Solution:
Arithmetic sequence : Sequence of terms in which difference between one term and the next is a constant.
This is also called Arithmetic Progression AP
Arithmetic sequence can be represented in the form :
a, a + d , a + 2d , …………………………, a + (n-1)d
a = First term
d = common difference = aₙ-aₙ₋₁
nth term = aₙ = a + (n-1)d
Sₙ = (n/2)(2a + (n - 1)d)
Sum of Arithmetic sequence (AP) is called Arithmetic series
26, 22, 18, 14, ...
a = 26
d = - 4 ( 22 - 26 = - 4 = 18 - 22)
Terms = n
Sₙ = -64
Sₙ = (n/2)(2a + (n - 1)d)
=> -64 = ( n/2)(2 * 26 + (n - 1)(-4))
=> -64 = n ( 26 - 2n + 2)
=> --64 = n ( 28 - 2n)
=> -32 = n ( 14 - n)
=> -32 = 14n - n²
=> n² - 14n - 32 = 0
=> n² - 16n + 2n - 32 = 0
=> n (n - 16) + 2(n - 16) = 0
=> (n - 16)(n + 2) = 0
=> n = 16 , n = -2
Terms can not ne negative
n = 16
16 terms must be taken for the sum to be -64
Learn More:
In an infinite g.P. Each term is equal to three times the sum of all the ...
brainly.in/question/9079152
if s1,s2,s3...sp are the sum of infinite geometric series whose first ...
brainly.in/question/5796750
How to derive sum of n terms of an A.P? - Brainly.in
brainly.in/question/7849150
In an A.P if sum of its first n terms is 3n square +5n and it's Kth term ...
brainly.in/question/8236011