3.
Find the sum of first 16 terms of an Arithmetic Progression whose
4th and 9th terms are 15 and - 30 respectively.
Answers
Answer:
MATHS
Find the sum of first 17 terms of an A.P., where 4th and 9th terms are −15 and −30, respectively.
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ANSWER
T
4
=−15=a+(4−1)d
−15=a+(3)d (1)
T
9
=−30=a+(9−1)d
−30=a+(8)d (2)
Where a is the first term of A.P and d is the difference between two terms.
(2)-(1) gives
−15=5d
d=−3 (3)
Substiyutin (3) in (1)
−15=a+3(−3)
−15=a−9
a=−6
S
17
=
2
n
(2a+(n−1)d)
S
17
=
2
17
(2(−6)+(17−1)d)
S
17
=
2
17
(−12+(16)(−3))
S
17
=
2
17
(−60)
S
17
=17×−30=−510
Hence the correct answer is −510
Answer:
-408
Step-by-step explanation:
4th term = a + 3d = 15
9th term = a + 8d = -30
- - +
------------------------
-5d = 45
d = -9
so, a = 15-3(-9) = 15+27 = 42
so, A16 = a+(n-1)d = 42 + (16-1)(-9)
= 42-135
= -93
so, S16 = 8(42-93)
= 8(-51)
= -408 ... ans