Question

1+5+9.......+x=1770,find the value of x
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Answer 1

Here it's given that the sum of first a few terms of an arithmetic series is 1770. Here,

1 + 5 + 9 +......+ x = 1770,

the arithmetic series has a first term 1 and common difference 4. So the algebraic expression of this AP, or the n'th term, is 4n - 3.

For an AP having first term a and common difference d, if a_n is the n'th term, then sum of first n terms is,

For an AP having first term a and common difference d, if a_n is the n'th term, then sum of first n terms is, S_n = n (a + a_n) / 2

Thus, let x = 4n - 3. Then,

n (1 + x) / 2 = 1770

n (4n - 2) = 3540

4n² - 2n - 3540 = 0

n = [2 ± √(4 - (4 × 4 × - 3540))] / 8

n = (2 ± 238) / 8

Since n > 0,

n = 30

Therefore,

x = 4 × 30 - 3 = 117

Hence 117 is the answer.

#answerwithquality

#BAL

Answer 2

Answer:

1+5+9+......+x=1770