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The value of x if 1 + 6 +11 + 16 +...+ x = 148 is,

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answer is C.

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Detailed Solution

Given equation is 1 + 6+11 + 16 +...+x= 148.
We need to find the value of x.
We know,

S n = n 2 2 a + n − 1 d

The first term is a=1.
The common difference is d.
The number of terms are n.
The common difference is,

d = 6 − 1 ⇒ d = 5

Therefore,

S_{n}

is,

148 = n 2 21 + n − 1 5 ⇒ 148 = n 2 2 + 5 n − 5 ⇒ 296 = n 5 n − 3 ⇒ 5 n 2 − 3 n − 296 = 0

⇒ 5 n 2 − 3 n − 296 = 0 ⇒ 5 n 2 − 40 n + 37 n − 296 = 0 ⇒ 5 n n − 8 + 37 n − 8 = 0 ⇒ 5 n + 37 n − 8 = 0

⇒ 5 n + 37 = 0 ⇒ 5 n = − 37 ⇒ n = − 375

And,

n − 8 = 0 ⇒ n = 8

Take a positive value. So the number of terms is n=8.
Substitute 1 for a, 5 for d, 8 for n, and x for

a n

in the equation

a n = a + n − 1 d

to find the value of n,

x = 1 + 8 − 1 5 ⇒ x = 1 + 7 × 5 ⇒ x = 1 + 35 ⇒ x = 36

The value of x is 36.
Hence, option 3 is correct.

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