Question

This is progressioni need to know C plsssssthankssssssssssßsssssss​

Answer 1

Answer:

$l = 28$

Step-by-step explanation:

Given

$S = \sum (2k - 3); k = 4\ to\ l$

Required

What is l when S = 725

This can be solved using Sum of n terms of an AP;

$S_n = \frac{n}{2}(T_1 + T_n)$

Where

$S_n = 725$

$T_1 = first\ term$

To get T1; we substitute 4 for k in 2k - 3

$T_1 = 2 * 4 - 3$

$T_1 = 8 - 3$

$T_1 = 5$

$T_n = last\ term$

To get Tn; we substitute l for k in 2k - 3

$T_n = 2 * l - 3$

$T_n = 2l - 3$

n = the number of terms;

Since k = 4 to l, then

$n = l - 4 +1$

$n = l - 3$

Substitute these values in $S_n = \frac{n}{2}(T_1 + T_n)$

$725 = \frac{l-3}{2}(5 + 2l - 3)$

Collect Like Terms

$725 = \frac{l-3}{2}(2l + 5- 3)$

$725 = \frac{l-3}{2}(2l + 2)$

Open the bracket

$725 = \frac{l-3}{2} * 2l + \frac{l-3}{2} * 2$

$725 = (l-3) * l + (l-3)$

$725 = l^2-3l + l-3$

$725 = l^2-2l -3$

Subtract 725 from both sides

$725 - 725 = l^2-2l -3 - 725$

$l^2-2l -3 - 725 = 0$

$l^2-2l - 728 = 0$

$l^2 + 26l - 28l - 728 = 0$

$l(l + 26) - 28(l + 26) = 0$

$(l - 28)(l + 26) = 0$

$l - 28 = 0$ or $l + 26 = 0$

$l = 28$ or $l = -26$

But l must be positive;

Hence, $l = 28$