The first and last term of an AP are 1 and 121 respectively. If the sum of the series is 671,find a) the number of terms (n) in the AP b) the common difference between them

(a)11

(b)12

Step-by-step explanation:

The first term, a = 1

The last term, l=121

Sum of the series,

Given an arithmetic series where the first and last term is known, its sum is calculated using the formula:

Substituting the given values, we have:

(a)There are 11 terms in the arithmetic progression.

(b)We know that the 11th term is 121

The nth term of an arithmetic progression is derived using the formula:

Therefore:

121=1+(11-1)d

121-1=10d

120=10d

d=12

The common  difference between them is 12.

b

step-by-step explanation:

the system of inequity is

step-by-step explanation:

from the given graph it is noticed that we have two related lines. one is solid and another is dashed.

if a line passing through two points, then the equation of line is

the solid line passing through the points (0,4) and (4,0).

the related equation of solid line is .

similarly, find the related equation of dashed line. the dashed liune passing through the points (0,0) and (3,1).

the related equation of dashed line is

from the given graph it is noticed that the point (0,1) lies on the shaded region, therefore the point (0,1) must be satisfied by the related equations.

check the related equations by the point (0,1).

this statement is true if the sign of inequality is < instead of equality. since it is an solid line therefore the sign of inequality will be . the required inequality is

similarly, check the second related equation.

it is a dashed line, so this statement is true if the sign of inequality is > . the required inequality is