In an A.P. if the first term is 22, the common difference is – 4 and

1.	In an A.P. if the first term is 22, the common difference is – 4 and the sum to n terms is 64, find n.
Answer» a = 22, d = -4 S_n = 64 64 = \(\frac{n}{2}\) (2a + (n – 1) d) n [44 – (n – 1)4] = 128 n (44 – 4n + 4) = 128 48n – 4n² = 128 n² – 12n + 32 = 0 n² – 8n – 4n + 32 = 0 (n – 8) (n – 4) = 0 n = 8 or n = 4

In an A.P. if the first term is 22, the common difference is – 4 and the sum to n terms is 64, find n.

Answer»

a = 22, d = -4

S_n = 64

64 = \(\frac{n}{2}\) (2a + (n – 1) d)

n [44 – (n – 1)4] = 128

n (44 – 4n + 4) = 128

48n – 4n² = 128

n² – 12n + 32 = 0

n² – 8n – 4n + 32 = 0

(n – 8) (n – 4) = 0

n = 8 or n = 4