19. The sum of first n terms of an AP is 3n² - 5, find the third term of the AP.
Answers
Answered by
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Sum of first n terms of an AP = 3n²-5
The third term = a3
By using formula :-
putting the equation (2) and (3) into (1)
we get,
•°• 15 is the 3rd term of the given AP.
Answered by
0
Answer:
The third term of AP is 5 .
Step-by-step explanation:
Given as :
The sum of first n terms of an AP is 3 n² - 5
For Arithmetic progression
Sum of n term = = [ 2 a + ( n - 1 ) d ]
= 3 n² - 5
= 3 (n – 1)² + 5
Or, = 3 × [ n² + 1 - 2 n ] + 5
Or, = 3 n² - 6 n + 3 + 5
∴ = 3 n² - 6 n + 8
Again
term = -
i.e = ( 3 n² - 5) - ( 3 n² - 6 n + 8 )
Or, = ( 3 n² - 3 n² ) + 6 n - 8 - 5
Or, = 0 + 6 n - 13
∴ = 6 n - 13
So, The nth term = 6 n - 13
Now, for n = 1
= 6 × 1 - 13 = - 7
similarly
= 6 × 3 - 13 = 5
So, The third term = = 5
Hence, The third term of AP is 5 . Answer
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