If the sum of first 5 terms of an AP is 25 and that of 19 terms is 361, find the sum
of first n terms.
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Answer:
Sum of n terms in A.P.
Sn =(n/2)[2a + (n- 1)d]
Given, S8=64
S19=361.
S8=4*(2a+7d)
==>4*(2a+7d)=64
==>2a+7d=16——→1
S19=19/2 * (2a+18d)
==>19 * (a+9d)=361.
==>a+9d=19.——->2
2* eq2 - eq1,
2a+18d-2a-7d=38–16
==>11d=22
Therefore d=2.
Substitute d value in eq 2,
a+18=19
==>a=1.
Now, we have to calculate the Sum of first 20 terms,
S20=20/2 *[2*1+(19)*2]
S20=10* [2+38]
S20=400.
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