The sum of the first 25 terms of an A.P. is 1700, while its common difference is 6. What is the 31st term of the
10.
A.P.?
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Step-by-step explanation:
Sₙ = n/2[2a + (n-1)d]
1700 = 25/2[2a + 24d]
=> 2a + 24d = 1700 * 2/25
=> 2a + 24d = 136
=> 2a + 24*6 = 136
=> 2a = 136 - 144
=> 2a = -8
=> a = -4.
nth term of AP is given by tₙ = a + (n-1)d
31st term is t₃₁ = -4 + (31 - 1)6 = - 4 + 180 = 176.
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