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Question
The sum of the first 9 terms of an AP is 81 and that of its first 20 terms is 400. Find the first term and common difference of the AP.
Solution
Here , a = 4 , d = 7 and l = 81
Let the nth term be 81.
Then Tn = 81
⇒ a +(n-1) d = 4+(n-1) 7 =81
⇒ (n-1) 7=77
⇒ (n-1) = 11
⇒ n = 12
Thus, there are 12 terms in the AP.
The sum of n terms of an AP is given by
`s_n = n/2 [ a +l]`
∴ `s_12 = 12/2 [4+81] = 6 xx85 = 510`
Thus, the required sum is 510.
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