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Question -

If the 5th term of an A.P. is 31 and 25th term is 140 more than the 5th term, find the A.P. [BTE2015]



Answer -

We know that,
Tn = a + (n – 1 )d
T5 = a + 4d => a + 4d = 31 ……(i)
and T25 = a + 24d
=>a + 24d = 140 + T5
=> a + 24d = 140 + 31 = 171 …..(ii)
Subtracting (i) from (ii),
20d= 140
and a + 4d = 31
=> a + 4 x 7 = 31
=> a + 28 = 31
=> a = 31 – 28 = 3
a = 3 and d = 7
AP will be 3, 10, 17, 24, 31, ……..

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