How many terms of the ap: -15, -13, -11, ..... Must be taken to give a sum of -55? Explain the reason for double answer.
Answers
Answer:
either 5 or 11 terms
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Step-by-step explanation:
a = -15
d = -13 - (-15) = 2
S = (n/2)(a + L)
n = number of terms L = last term
L = a + (n-1)d
L = -15 + (n-1)2
L = 2n - 17
S = -55
-55 = (n/2)(-15 + 2n-17)
-110 = (n) ( 2n -32)
-55 = n (n-16)
n^2 - 16n + 55 = 0
n^2 - 5n - 11n + 55 = 0
(n-5)(n-11) = 0
n = 5 or n =11
so either 5 terms or 11 terms
Verification :
for 5 terms
-15 , -13 , -11 , - 9 , -7
Sum = -55
for 11 terms
-15 , -13 , -11 , -9 , -7 , -5 , -3 , -1 , 1 , 3 , 5
Sum = -55 (as out of last 6 terms 3 terms are positive and 3 terms are negative with same value respectively)
Hence verified
Please mark the answer as "The Brainliest answer" if it helps
Answer:
Step-by-step explanation:
a = -15
d = -13 - (-15) = 2
S = (n/2)(a + L)
n = number of terms L = last term
L = a + (n-1)d
L = -15 + (n-1)2
L = 2n - 17
S = -55
-55 = (n/2)(-15 + 2n-17)
-110 = (n) ( 2n -32)
-55 = n (n-16)
n^2 - 16n + 55 = 0
n^2 - 5n - 11n + 55 = 0
(n-5)(n-11) = 0
n = 5 or n =11
so either 5 terms or 11 terms
Verification :
for 5 terms
-15 , -13 , -11 , - 9 , -7
Sum = -55
for 11 terms
-15 , -13 , -11 , -9 , -7 , -5 , -3 , -1 , 1 , 3 , 5
Sum = -55 (as out of last 6 terms 3 terms are positive and 3 terms are negative with same value respectively)
Hence verified