Question

in an ap the ratio of the 7th term to the 10th term is -1 if the 16th term ìs -15 what is the 3rd term
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Answer 1

Here is the Answer :

$\frac{7th \: term}{10th \: term} = - 1 \\ 7th \: term \: = - 10th \: term$

Because: (7th term = a +6d)

and

(10th term = a +9d)

So,

a + 6d = - a - 9d

2a = - 15d

$a = \frac{- 15d}{2} \: \: \: \: \: \: \: (eq \: 1st)$

Now

16 th term = - 15

16 th term = - 15

a + 15d = - 15

From Eq 1st value of a

$\frac{ - 15d}{2} + 15d = - 15$

$\frac{ - 15d + 30d}{2} = - 15 \\ 15d = - 30 \\ d = - 2$

Now putting the value of d in Eq 1st

$a = \frac{ - 15d}{2} \\ a = \frac{ - 15 \times - 2}{2} \\ \\ a = 15$

So, 3rd term = a + 2d

= 15 + 2d

= 15 + 2(- 2) = 11

MARK BRAINLIEST