How many term of arithmetic progression 45 39 33 must be taken so that their sum is 180 explain the double answer
Answers
Answer:
The sum will be 180 either by taking 6 terms or by taking 10 terms
Step-by-step explanation:
Given,
first term = a = 45
common difference = d = -6
hence sum of an AP is given by,
S= n/2[2a + (n-1)d]
=> 180 = n/2[ 90 - 6(n-1)
=> 360 = 96n - 6n²
=> 6n² - 96n + 360 = 0
=> n² - 16n + 60 = 0
=> (n-6)(n-10) = 0
=> n = 6 or n = 10
Hence the sum will be 180 either by taking 6 terms or by taking 10 terms because after 8th term the remaining terms are -ve, so they cancel some of the positive terms,
AP = 45 , 39, 33, 27, 21, 15, 9, 3, -3, -9
hence sum of first 6 terms = [ 45 + 39 + 33 + 27 + 21 + 15] = 180
sum of first 10 terms = [ 45 + 39 + 33 + 27 + 21 + 15 + 9 + 3 - 3 -9] = 180
Answer:
Sn = 180
n/2 [90 + (n - 1)(-6)] = 180
90n – 6n2 + 6n = 360
⇒ 6n2 – 96n + 360 = 0
⇒ 6[(n – 6)(n – 10)] = 0
⇒ n = 6, n = 10
Sum of a7, a8, a9, a10 = 0
∴ n = 6 or n = 10
Step-by-step explanation:
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