Question

Find the value x -2+5+8+...+x=155

Answer 1

answer........................

Answer 2

Answer:

29

Step-by-step explanation:

Given:

x -2+5+8+...+x=155

To find:

Value of x

Solution:

An exclusive type of sequence for which we can locate and derive the formula for the nth term is referred to as a progression. The Arithmetic Progression, or AP, is the most often used sequence in mathematics and comprises formulae that are relatively simple to comprehend.

The first term of the AP, its common difference, and the nth term are the most frequently utilised terms in an arithmetic progression (AP) for a given series or sequence.

The following formula can be used to determine the nth term of an arithmetic progression:

where a = a + (n - 1)d

The first term is "a," the second is "d," the third is "n," and the fourth is "an."

It is essential to emphasise that an arithmetic progression's sequence depends on its common difference, or d.

The terms of an AP will go toward the positive side of infinity if the common difference, or d, is positive. The terms of AP, on the other hand, will converge to the negative side of infinity if the common difference, or d, is negative.

a = 2

d = 3

$S_n=\frac{n}{2} [2a+(n-1)d]\\155=\frac{n}{2}[2(2)+(n-1)d]\\310=n(4+3n-3)\\310=n(1+3n)\\3n^{2}+n-310=0\\ 3n^{2}-30n+31n-310=0\\3n(n-10)+31(n-10)=0\\n=10$

l=a+(n-1)d

=2+9(3)

x=29

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