Question

please answer this question ​

Answer 1

Step-by-step explanation:

We know that the n

th

term of the arithmetic progression is given by a+(n−1)d

Given that the 10 times the 10

th

term is equal to 15 times the 15

th

term

Therefore, 10(10

th

term)=15(15

th

term)

⟹10(a+(10−1)d)=15(a+(15−1)d)

⟹10(a+9d)=15(a+14d)

⟹10a+90d=15a+210d

⟹15a−10a=90d−210d

⟹5a=−120d

⟹a=−24d ------(1)

The 25

th

term is a+(25−1)d=a+24d=−24d+24d=0

Therefore, the 25

th

term of the A.P. is zero

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