Question
If 8 times the 8th term of an AP is equal to 15 times the 15th term of the AP, then the 23rd term of the AP is ___.
Answer: Option C
:
C
Given,
8a8=15a15.
Since the nth term of an AP of first term a and common difference d is given by
an=a+(n−1)d, we have
8[a+(8−1)d]=15[a+(15−1)d].⇒8(a+7d)=15(a+14d)⇒8a+56d=15a+210d⇒7a+154d=0⇒a+22d=0⇒a+(23−1)d=0
Hence, the 23rd term of the AP is zero.
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:
C
Given,
8a8=15a15.
Since the nth term of an AP of first term a and common difference d is given by
an=a+(n−1)d, we have
8[a+(8−1)d]=15[a+(15−1)d].⇒8(a+7d)=15(a+14d)⇒8a+56d=15a+210d⇒7a+154d=0⇒a+22d=0⇒a+(23−1)d=0
Hence, the 23rd term of the AP is zero.
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