Which term of the AP 5, 15, 25, …will be 130 more than its 31st term?
Question:

Which term of the AP 5, 15, 25, …will be 130 more than its 31st term?

Solution:

Here, a = 5 and d = (15 – 5) = 10
The 31st term is given by
T31 = a + (31 – 1)d = a + 30d = 5 + 30 ⨯ 10 = 305
∴ Required term = (305 + 130) = 435
Let this be be the nth term.
Then Tn = 435
​⇒ 5 + (– 1) ⨯ 10 = 435
⇒ 10n = 440
⇒ n = 44
Hence, the 44th term will be 130 more than its 31st term.  

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