Answer :
Answer:
13
Step-by-step explanation:
The sum to n terms of an AP is
[tex]S_{n}[/tex] = [tex]\frac{n}{2}[/tex] [ 2a₁ + (n - 1)d ]
where a₁ is the first term and d the common difference
Here [tex]S_{n}[/tex] = 26, a₁ = - 10 and d = - 8 - (- 10) = - 8 + 10 = 2 , thus
[tex]\frac{n}{2}[/tex] [ (2 × - 10) + 2(n - 1) ] = 26 ( multiply both sides by 2 )
n(- 20 + 2n - 2) = 52
n(- 22 + 2n) = 52
- 22n + 2n² = 52 ( subtract 52 from both sides )
2n² - 22n - 52 = 0 ( divide through by 2 )
n² - 11n - 26 = 0 ← in standard form
(n - 13)(n + 2) = 0 ← in factored form
Equate each factor to zero and solve for n
n - 13 = 0 ⇒ n = 13
n + 2 = 0 ⇒ n = - 2
However, n > 0 , thus number of terms is 13