find the sum of first 17 terms of and AP whose 4th and 9th terms are -15 and -30 respectively
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Answered by
162
Sum of 17 terms = (a1 + a17)*17/2.
Need to find first term & common difference.
a4 = -15
a + 3d = -15
a9 = -30
a + 8d = -30
Solving it, 5d = -15, d=-3//
Therefore, a = -6
Therefore a17 = a + 16d = -6 - 48 = -54
Therefore, sum of first 17 terms = (-6 -54)*17/2 = -510//
Need to find first term & common difference.
a4 = -15
a + 3d = -15
a9 = -30
a + 8d = -30
Solving it, 5d = -15, d=-3//
Therefore, a = -6
Therefore a17 = a + 16d = -6 - 48 = -54
Therefore, sum of first 17 terms = (-6 -54)*17/2 = -510//
vee1:
If u r happy with the answer, pls mark as Brainliest. Thank you!
oh yeah....thanks Vee1 i guess my mistake was the value of my "a" instead of (-6) I wrote (-9)..... thnx a lot.... sorry guys that's my bad
Answered by
137
Answer:
Step-by-step explanation:
Solution :-
Let the first term be a and the common difference be d of the given A.P.
a(n) = a + (n - 1)d
Now, According to the Question,
a(4) = a + 3d = - 15 ..... (i)
a(9) = a + 7d = - 30 .....(ii)
Subtracting Eq (i) and (ii), we get
⇒ (a + 8d) - (a + 3d) = - 30 - (- 15)
⇒ 5d = - 15
⇒ d = - 15/5
⇒ d = - 3
From (i)
⇒ a + 3d = - 15
⇒ a + 3(- 3) = - 15
⇒ a = - 15 + 9
⇒ a = - 6
Again, S(17) = 17/2[2 × (- 6) + (17 - 1) (- 3)]
S(17) = 17/2[- 12 + 16 × (- 3)]
⇒ S(17) = 17/2[- 12 - 48]
⇒ S(17) = 17/2[- 60]
⇒ S(17) = 17 × (- 30)
⇒ S(17) = - 510
Hence, the sum of 17 terms of an A.P. is - 510.
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