Question

Find The sum of 35 term of an ap whose 2 term is 14 and 3 term is 18

Answer 1

Answer:

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Answer 2

ᴄᴏɴᴄᴇᴘᴛ ᴜsᴇᴅ :-

• A sequence is said to be in AP (Arithmetic Progression), if the difference between its consecutive terms are equal.

• The nth term of an AP is given as ;

T(n) = a + (n-1)•d , where a is the first term and d is the common difference.

• The common difference of an AP is given as ;

d = T(n) - T(n-1)

• If the number of terms in an AP is n ( where n is odd ) ,then there will be a single middle term.

Also, [(n+1)/2]th term will be its middle term.

• If the number of terms in an AP is n ( where n is even ) ,then there will be two middle terms.

Also, (n/2)th and (n/2 + 1)th terms will be its middle terms.

• The sum up to nth terms of an AP is given as ;

S(n) = (n/2)•[2a + (n-1)•d] where a is the first term and d is the common difference.

• The nth term of an AP is also given as ;

T(n) = S(n) - S(n-1)

Sᴏʟᴜᴛɪᴏɴ :-

→ T(2) = 14

→ T(3) = 18

→ d = T(n) - T(n-1)

→ d = 18 - 14

→ d = 4.

So,

→ T(1) = a = T(2) - d

→ a = 14 - 4

→ a = 10 .

Therefore,

→ Sn = (n/2)•[2a + (n-1)•d]

→ S(35) = (35/2)[2*10 + (35-1)4]

→ S(35) = (35/2)[ 20 + 34*4 ]

→ S(35) = (35/2)[ 20 + 136 ]

→ S(35) = (35/2)[ 156 ]

→ S(35) = 35 * 78

→ S(35) = 2730 (Ans.)