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Q.

Find the sum: 25 + 28 + 31 +… + 100.


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a

1234

b

1625

c

1742

d

1655 

answer is B.

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Detailed Solution

Given sequence is 25 + 28 + 31 +… + 100.
From the given sequence we can see that,
First term of AP (a) = 25,
common difference (d) = 28-25 = 3.
We know that,
tn = a + (n-1)d, where tn is the nth term of AP.
⇒ 100 = 25 + (n-1)3
⇒ 100 – 25 = 3(n-1)
⇒ 3(n-1) = 75
⇒ (n-1) = 25
⇒ n =26
Hence, the number of terms in the given AP are 26.
Now, sum of AP = n 2 a+l  , where l is the last term of AP.
⇒ Sum = 26 2 25+100  
⇒ Sum = 13 125  
⇒ Sum = 1625  
Hence, the sum of 25 + 28 + 31 +… + 100 = 1625.
Therefore, the correct answer is option (2).
 
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