Question

how many term of AP. 24,21,18,........must be taken so that their sum is 78

Answer 1

Answer:

4 and 13

Step-by-step explanation:

a=24

d=-3

Sn=78=n/2(2a+(n-1)d)

156=n(48-3n+3)

156=51n-3n^2

3n^2-51n+156=0

n^2-17n+52=0

n=4,13

Answer 2

$\huge\sf\red{Here,}$

$\large\tt\purple{a=24}$

$\large\tt\purple{d=21-24=-3}$

$\large\tt\purple{Sn=78}$

$\large\tt\red{We\:need\:to\:find\:n.}$

$\longrightarrow$$\large\tt\purple{Sn=\frac{n}{2} (2a + (n - 1)d)}$

$\longrightarrow$$\large\tt\purple{78 = \frac{n}{2} (48 + (n - 1)( - 3))}$

$\longrightarrow$$\large\tt\purple{ \frac{n}{2} (51 - 3n)}$

$\longrightarrow$$\large\tt\purple{{3n}^{2} - 51n + 156 = 0}$

$\longrightarrow$$\large\tt\purple{{n}^{2}-17n+52=0}$

$\longrightarrow$$\large\tt\purple{(n-4)(n-13)=0}$

$\longrightarrow$$\large\tt\purple{n=4or13}$

Both values of n are admissible, So, rhe number of terms is either 4 or 13