Question

if seven times the seventh term of an AP . is equal to ten times the tenth term then show that the seventeenth term of an AP is zero??
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Answer 1

Hey mate.
========

Given ,

Seven times the seventh term of an AP . is equal to ten times the tenth term.

ie. 7 × a (7) = 10 × a (10)

Now,

7 ( a + 6d ) = 10 ( a + 9d)

=> 7a + 42d = 10a + 90d

=> 7a - 10a = 90d - 42d

=> -3a = 48d

=> a = 48d / -3

=> a = -16d........(1)

We now need to show that the seventeenth term of an AP is 0

Thus,

a (17)

= a + 16d

= (-16d ) + 16d [ From (1) ]

= 0

Hence, a (17) = 0 , Shown

#racks

Answer 2

Hello Frnd

We know that the terms of AP is denoted by
" an "

Here 7th term = a7
10th term = a10

Now
According to question

7(a7) = 10 (a10)
7( a + 6d) = 10(a + 9d)

7a + 42d = 10a +90d
10a - 7a = - 48d
3a = - 48d

a = - 48d/3
a= - 16d ........ (1)

As we know

a17 = a +16d

Consider (1), we get
a +16d = 0

Hence proved



hope it helps you
#jerri