Question

solve the equation
1+5 +9++13.........+x=1326
​

Answer 1

Answer:

x (last term) = 101

No. of terms = 26 terms

Step-by-step explanation:

This is an AP with a common difference (d) of 9 - 5 = 5 -1 => 4

Now, the sum of the AP is given as 1326.

Now, we know that sum of AP = [n/2][2a + (n - 1)d] or [n/2][a + l]

First, we will find the no. of terms by using the first formula.

=> [n/2][2(1) + (n - 1)4] = 1326

=> [n/2][2 + 4n - 4] = 1326

=> [n/2][4n - 2] = 1326

=> (n)(2n - 1) = 1326

=> 2n² - n - 1326 = 0

Its roots are 26 and -25.5.

As no. of terms can't be positive, no. of terms are 26.

Putting this in the second formula,

(n/2)(a + l)

=> (26/2)(1 + x) = 1326

=> 13(x + 1) = 1326

=> 13x + 13 = 1326

=> 13x = 1326 - 13 => 1313

∴ x = 1313/13 => 101

Thus, x or the last term is 101 and the number of terms is 26.