Question

7: Inan A.P. sum of three consecutive terms is 27 and their product is 504, find the terms.
(Assume that three consecutive terms in A.P. are a-d, a, a + d.)
Find four consecutive terms in an A.P. whose sum is 12 and sum of 3 and 4th term
(Assume the four consecutive terms in A.P. are a-d, a, a + d, a + 2d.)
If the 9 term of an A.P. is zero then show that the 29th term is twice the 19th term.
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Answer 1

ᴀssᴜᴍᴇ ᴛʜᴀᴛ ᴛʜʀᴇᴇ ᴄᴏɴsᴇᴄᴜᴛɪᴠᴇ ᴛᴇʀᴍs ɪɴ ᴀ.ᴘ. ᴀʀᴇ ᴀ – ᴅ , ᴀ , ᴀ + ᴅ .

ɪᴛ ɪs ɢɪᴠᴇɴ ᴛʜᴀᴛ

sᴜᴍ ᴏғ ᴛʜʀᴇᴇ ᴄᴏɴsᴇᴄᴜᴛɪᴠᴇ ᴛᴇʀᴍs = 27

ᴘʀᴏᴅᴜᴄᴛ ᴏғ ᴛʜʀᴇᴇ ᴄᴏɴsᴇᴄᴜᴛɪᴠᴇ ᴛᴇʀᴍs = 504

(ᴀ−ᴅ)+ᴀ+(ᴀ+ᴅ)=27

⇒3ᴀ=27

⇒ᴀ=9

(ᴀ−ᴅ)×ᴀ×(ᴀ+ᴅ)=504

⇒(9−ᴅ)×9×(9+ᴅ)=504

⇒81−ᴅ2=56

⇒ᴅ2=81−56

⇒ᴅ2=25

⇒ᴅ=±5

ᴡʜᴇɴ ᴅ = 5,

ᴛʜᴇ ᴛᴇʀᴍs ᴀʀᴇ 9, 14, 19.

ᴡʜᴇɴ ᴅ = –5,

ᴛʜᴇ ᴛᴇʀᴍs ᴀʀᴇ 9, 4, –1.

Answer 2

Step-by-step explanation:

Solution. Assume that three consecutive terms in A.P. are a – d , a , a + d . When d = 5, The terms are 9, 14, 19

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