Q. 94.0( 7 Votes )

Find the sum of first 20 terms of the arithmetic series in which 3rd term is 7 and 7th term is 2 more than three times its 3rd term.

Answer :

First term = a


Common difference = d


3rd term = a + (3–1)d = a + 2d


7th term = a + (7–1)d = a + 6d


Now, 3rd term = 7


a + 2d = 7 ………………………(1)


And, 7th term = 3 × (3rd term) + 2


a + 6d = 3(a + 2d) + 2


a + 6d = 3a + 6d + 2


2a = –2


a = –1


Putting value of a in (1)


( –1) + 2d = 7


2d = 8


d = 4


Sum of terms =


Sum of terms =


Sum of terms =


Sum of terms = 740


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