Question

Which term the 10th term of an AP is equal to 15 times the 15th term show that 25th term of the AP is zero ​

Answer 1

Answer:

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

Answer 2

Step-by-step explanation:

HEY MATE ........

Let a be the first term and d be the common difference of the AP. Then,

$10 \times a {10} \: \: = \: \: 15 \times a {15}</strong><strong>. </strong><strong>{given} \\ \\ = 10{a + 9d} = 15{a + 14d}</strong><strong>. </strong><strong> </strong><strong> </strong><strong>(</strong><strong>{{n} \</strong><strong>(</strong><strong>: a + {n - 1}d} </strong><strong>)</strong><strong> </strong><strong>)</strong><strong>\\ \\ 2{a + 9d} \: = \: 3{a + 14d} \\ \\ 2a + 18d = 3a + 42d \\ \\a = - 24d \\ \\ a + 24d = 0 \\ \\ a + {25 - 1}d = 0 \\ \\ a {25} = 0 \\ \\ hence \: </strong><strong>the</strong><strong> </strong><strong>25th \: term \: of \: the \: ap \: = 0$