Find the sum of first 17 terms of an AP whose 4th and 9th terms are - 15 and - 30, respectively.


Let the a be first term and d be common difference of an AP


Given,


4th term = - 15


a + 3d = - 15 [ using an = a + (n - 1)d]


a = - 3d - 15 [ eqn 1]


9th term = - 30


a + 8d = - 30


- 3d - 15 + 8d = - 30 [ using 1]


5d = - 15


d = - 3


putting this value in eqn 1 we get


a = - 3 (- 3) - 15


= 9 - 15 = - 6


Also we know,


Sum of n terms,





= 17 (- 30)


= - 510


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