Question

The sum of n terms of an ap is 3n+5n.find the ap hence find its 16th term

Answer 1

$\mathtt{\huge{\underline{\purple{Question\:?}}}}$

The sum of n terms of an AP is 3n + 5. Find the AP. Hence find its 16th term.

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Given :-

• Sum of n terms of an AP is 3n + 5

To Find :-

• AP

• 16th term.

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$\mathtt{\huge{\underline{\purple{Answer\:?}}}}$

1st term, a = 3(1) + 5

=> 3 + 5

=> 8

2nd term = 3(2) + 5

=> 6 + 5

=> 11

Common difference d = 2nd term - 1st term

=> 11 - 8

=> 3

Hence, AP = 8,11,14......

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Tn = a +(n - 1)d

=> 8 + (16 - 1)3

=> 8 + 45

=> 53

Hence, 16th term of AP is 53.

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Answer 2

ϙᴜᴇsᴛɪᴏɴ :-

ᴛʜᴇ sᴜᴍ ᴏғ ɴ ᴛᴇʀᴍs ᴏғ ᴀɴ ᴀᴘ ɪs 3ɴ + 5. ғɪɴᴅ ᴛʜᴇ ᴀᴘ. ʜᴇɴᴄᴇ ғɪɴᴅ ɪᴛs 16ᴛʜ ᴛᴇʀᴍ.

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ɢɪᴠᴇɴ :-

• sᴜᴍ ᴏғ ɴ ᴛᴇʀᴍs ᴏғ ᴀɴ ᴀᴘ ɪs 3ɴ + 5

ᴛᴏ ғɪɴᴅ :-

• ᴀᴘ

• 16ᴛʜ ᴛᴇʀᴍ.

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ᴀɴsᴡᴇʀ

1sᴛ ᴛᴇʀᴍ, ᴀ = 3(1) + 5

=> 3 + 5

=> 8

2ɴᴅ ᴛᴇʀᴍ = 3(2) + 5

=> 6 + 5

=> 11

ᴄᴏᴍᴍᴏɴ ᴅɪғғᴇʀᴇɴᴄᴇ ᴅ = 2ɴᴅ ᴛᴇʀᴍ - 1sᴛ ᴛᴇʀᴍ

=> 11 - 8

=> 3

ʜᴇɴᴄᴇ, ᴀᴘ = 8,11,14......

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ᴛɴ = ᴀ +(ɴ - 1)ᴅ

=> 8 + (16 - 1)3

=> 8 + 45

=> 53

ʜᴇɴᴄᴇ, 16ᴛʜ ᴛᴇʀᴍ ᴏғ ᴀᴘ ɪs 53.

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