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nth Term of A.P

The first ter...

Question

The first term of an arithmetic progression is 15 and the last term is 85. If the sum of all terms is 750, what is the 6th term ?

A

30

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B

40

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C

45

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D

55

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Solution

The correct option is D 40
Here, sum of all terms $= 750$

$\frac{n}{2} (a + l) = 750$

$\frac{n}{2} (15 + 85) = 750$

$n = 15$

Now, $a_{15} = 85$

$a + 14 d = 85$

$d = 5$

Thus, $a_{6} = a + 5 d = 15 + 25 = 40$

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