OPEN CHALLENGE :
If you've brain then solve the question step by step specifically and correctly : ‘ Sum of first 55 terms in an A.P. is 3300, find its 28th term.
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OPEN CHALLENGE :
If you've brain then solve the question step by step specifically and correctly : ‘ Sum of first 55 terms in an A.P. is 3300, find its 28th term.
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Let us consider that the first term of the AP is a and the common difference for the AP is d.
We know that sum of n first n terms of the AP is
= n/2 × (a1 + an),
where a1 is the first term = a
and an = the nth term = a + (n - 1)d
= n/2 × [a + a + (n - 1)d]
= n/2 × [2a + (n - 1)d]
So, sum of the first 55 terms of the AP
= 55/2 × [2a + (55 - 1)d]
= 55/2 × [2a + 54d]
= 55/2 × 2 × (a + 27d)
= 55 × (a + 27d)
Given that,
55 × (a + 27d) = 3300
⇒ a + 27d = 60 .....(i)
So, the 28th term of the AP is
= a28
= a + (28 - 1)d
= a + 27d
= 60, by (i)
Thank you for your question.
Verified answer
S55 = n/2 [2a + (n - 1)d]3300 = 55/2 [2a +(55 - 1)d]
3300 = 55/2 (2a + 54d)
Now take 2 common
3300 = 55/2 × 2 (a + 27d)
3300/55 = a + 27d
a + 27d = a28 = 60
Thanks