How
many
terms of the
AP 24,21 must be taken
that the sum is 78?
Answers
Answer:
No. of term to be taken eithor 4 and 13 to get sum = 78.
Step-by-step Explanations :
Given : AP = 24,21..
Sn = 78
To find : n = ?
AP = 24, 21 , 18 ..
So,
First term of AP = (a) = 24, common difference (d) = (21 - 24) = -3
Let n no. of terms to be taken, So that sum = 78
So, sum of n terms of the AP,
Sn = n/2 × [2a + (n-1)d]
Substituting the given value in above formula we get,
= n/2 × (2 x 24 + (n-1) × (-3)
∴ n/2 × [48 + (n - 1) x (-3)] = 78
=> (48 +3 - 3n)n = 78 x 2
=> (51 - 3n)n = 78 x 2
=> (17 - n)n = 26 x 2 .. ( dividing by 3 )
=> n² - 17n = 52
=> n² - 17n + 52 = 0
=> n² - 13n - 4n + 52 = 0
=> n(n - 13) - 4(n - 13) = 0
=> (n - 13)(n - 4) = 0
∴ n = 4 and n = 13 (since, some terms be negative after zero)
Hence, no. of term to be taken eithor 4 and 13 to get sum = 78.