if the sum of 8 terms of an AP is equal to the sum of 5 terms of the AP then the sum of 13 terms is
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11th
Maths
Sequences and Series
Arithmetic Progression
If the sum of first 13 term...
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If the sum of first 13 terms of an AP is 21 and the sum of First 21 terms is 13, Show that sum of First 34 terms is −34.
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ANSWER
As we know that, the sum of n terms of an A.P. is given as
S
n
=
2
n
[2a+(n−1)d]
Therefore,
S
13
=
2
13
[2a+(13−1)d]
⇒21=13a+78d.....(1)
S
21
=
2
21
[2a+(21−1)d]
⇒13=21a+210d.....(2)
On solving (1)&(2), we get
a=
91
283
and d=
273
−68
Therefore,
S
34
=
2
34
[2×
91
283
+(34−1)(
273
−68
)]
⇒S
34
=17(
91
566
−
91
748
)
⇒S
34
=17(
91
566−748
)
⇒S
34
=17×(−
91
182
)=−34
Hence proved.
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