Question

If the first term of the AP is 4 and the sum of the first five terms is equal to one-fourth of the sum of the
next five terms, then find the 15th term?​

Answer 1

Answer:

If the first term of an A.P. is 2 and the sum of first five terms is equal to the one-fourth of the sum of next five terms, find the sum of first 30 terms?

Let common difference of given AP having first term a=2 be d

Now given that sum of first 5 terms = 14 (sum of next five terms )

⟹52[2(2)+(5–1)d]=14(102[2(2)+(10–1)d]−52[2(2)+(5–1)d])

⟹10[4+4d]=5[4+9d]−52[4+4d]

⟹20[4+4d]=10[4+9d]−5[4+4d]

⟹25[4+4d]=40+90d

⟹100+100d=40+90d

⟹10d=−60

⟹d=−6

Now Let sum of first 30 terms be S

⟹S=302[4+29(−6)]

⟹S=15(4–174)

⟹S=15(−170)

⟹S=−2550

Answer 2

Answer:

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