Question

answer this question plz​

Answer 1

Answer: 13 terms or 4 terms

Hope it helps

Answer 2

$\huge \bold{AP}$

AP is the abbreviation of arithmetic progression, it is the series in which digits occurs at regular intervals. The difference between the next term and previous term known as common difference is always constant.

FOR AN AP

$\boxed{S_n = \frac{n}{2}(2a + (n - 1)d)}$

Where a is first term,

d is commom difference

and n is the number of terms.

$\bold{ACCORDING \: TO \: QUESTION }$

Sum of nth term is 78

a = 24

d= 21- 24 = -3

$\boxed{S_n = \frac{n}{2}(2a + (n - 1)d)}$

$\mathsf{78 = \frac{n}{2}(2\times 24 + (n - 1) (-3))}$

$\mathsf{78 = \frac{n}{2}(2\times 24 + (n - 1) (-3))}$

$\mathsf{78 \times 2= n (48 -3n + 3)}$

$\mathsf{156= 48n -3n^{2} + 3n}$

$\mathsf{3n^{2} - 51n +156 = 0}$

On dividing equation by 3

$\mathsf{n^{2} - 17n +52 = 0}$

$\mathsf{n^{2} - 13n - 4n +52 = 0}$

$\mathsf{n(n- 13) - 4(n -13)= 0}$

$\mathsf{(n- 13)(n -4)= 0}$

On taking separately,

$\mathsf{n- 13= 0}$

$\boxed{\mathsf{n =13}}$

$\mathsf{n- 4= 0}$

$\boxed{\mathsf{n =4}}$

So, number of terms can either be 13 or 4.