Question

11) Find the sum of the arithmetic series if a, = 5, 4, = -160, and n = 21. -4706 12) Find all the values of x and y for which 3, x, y is an arithmetic sequence and x, y, 8 is a geometric sequence. 222 222 13) Find the value of y that makes this a geometric sequence: y+1, y, y-4.

Answer 1

y Griven a y A.m. 3, n and is is in in s G.m. so n-3 a 2na 3 na yon Y+ 4+3 a - (In AP, ga, b, c is Progression, then b-azlob) and a tlod é nice ting na ge in w we got y2 = uya12 y²-44-12 - y ² - 6y +24 -12 0 (96)(4+2) = 0 y=6 , ya-2 Put y=6 im and y=-2 in ý we a na 6+3

13 ся! Чт, -ч - are in Geometta selvenu .. ( If a, b, c are in G. P. I then be a 1 2 3 - 2 15 t ) У 2 1 - ич + - о - - 2y - ч 73 -- - -

11) Giren auas, a = -160 as an a a + (n-1)d whese an dst term na noq termi aus at curid au = a +3d -s -lii aga at (9-10) d Lag = a +8d - -160 - Subtracting is from du 8d-8d = a160-5 § da -165 Putting da -33 in i a - 99 25 Q. 104 Sum q 21 arithematic serie, s 120+ (0-1)xd] = 21 (2x104+ (21-1) +-33] 21 [ 208 .- 660] 226 462 x - 4746