Question

9. The sum of the 5th and the 9th terms of an AP is 30. If its 25th term is
ithree times its 18th term, find the AP *
2, 5, 8, 11...
3,5,7,9...
4, 6, 8, 10.
5,7,9,11...​

Answer 1

Answer:

4,6,8,10.

Explanation:

because the sum of 5th and 9th is 30

means, 2a +12b=30 eq --1

now, 25th term is three times 18 term

means, -2a - 27d = 0 eq - 2

therefore adding eq -1 and eq -2 we get the

answer......

hii plzz follow ❤️❤️

Answer 2

$\bf\huge\blue{\underline{\underline{ Question : }}}$

The sum of the 5th and the 9th terms of an AP is 30. If its 25th term is three times its 8th term, find the AP.

A) 2, 5, 8, 11...

B) 3,5,7,9...

C) 4, 6, 8, 10...

D) 5,7,9,11...

$\bf\huge\blue{\underline{\underline{ Solution : }}}$

★ Given that,

◼ Sum of 5th and 9th terms of an AP is 30.

• $\tt a_{5} + a_{9} = 30$

◼ 25th term of an AP is 3 times it's 8th term.

• $\tt a_{25} = 3(a_{8})$

★ To find,

• The AP series.

★ Let,

↪ ᴄᴀsᴇ - 1 :-

$\sf \implies a_{5} + a_{9} = 30$

$\sf \implies a + 4d + a + 8d = 30$

$\sf \implies 2a + 12d = 30 ..... (1)$

↪ ᴄᴀsᴇ - 2 :-

$\sf \implies a_{25} = 3(a_{8})$

$\sf \implies a + 24d = 3(a + 7d)$

$\sf \implies a + 24d = 3a + 21d$

$\sf \implies 3a + 21d - a - 24d = 0$

$\sf \implies 2a - 3d = 0$

$\sf \implies 2a =0 +3d$

$\sf \implies 2a =3d \: .....(2)$

• Substitute value of 2a in (1)

$\sf \implies 3d + 12d = 30$

$\sf \implies 15d = 30$

$\sf \implies d = \cancel{\cfrac{30}{15}}$

$\sf \implies d = 2$

• Substitute value of d in (2).

$\sf \implies 2a = 3(2)$

$\sf \implies 2a = 6$

$\sf \implies a = \cancel{\cfrac{6}{2}}$

$\sf \implies a = 3$

★ Now,

We have the first term and the common difference. Now, we can find the AP series.

$\tt AP\: series = a, a + d, a + 2d....$

• Substitute the both values.

$\sf \implies 3,3 + 2,3 + 2(2)...$

$\sf \implies 3,3 + 2,3 +4...$

$\sf \implies 3,5,7....$

# Hence,the correct option is B.

$\underline{\boxed{\rm{\purple{\therefore The\:AP\:series = 3,5,7....}}}}\:\orange{\bigstar}$

★ More Information,

$\boxed{\begin{minipage}{5 cm} AP Formulae : \\ \\ : \implies a_{n} = a + (n - 1)d \\ \\ :\implies S_{n} = \frac{n}{2} [ 2a + (n - 1)d ] \end{minipage}}$

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