Question:
How many terms of the AP : 9, 17, 25, . . . must be taken to give a sum of 636?
Answer:
Given A P : 9, 17,25, .............
Let number of terms in AP = n
Sum of n terms of AP = (n/2)*{2a + (n-1)*d}
=>636 = (n/2)*{2*9 + (n-1)*8}
=>636 = (n/2)*{18 + (n-1)*8}
=>636 = n*{9 + (n-1)*4}
=>636 = n*(9 + 4n-4)
=>636 = n*(4n + 5)
=>4n2 + 5n = 636
=>4n2 + 5n - 636 = 0
=>(n - 12)*(4n + 53) = 0
=> n=12, -53/12
Negative and fraction values are not possible for number of terms.
So number of terms in AP = 12
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