Question

for an ap if 4t4 = 7t7 find t11​

Answer 1

Answer:

Step-by-step explanation:

We know that tn = a+(n-1) d

t4= a+(4-1) d

t4= a+3d

16= 4a+12d ....... (Given) ... (1)

t7= a+(7-1) d

t7= a+6d

49 = 7a+42d ....... (Given) ..... (2)

Multiplying eq.(1) by 7 and eq.(2) by 2

112=28a + 84d .... (3)

98= 14a + 84d .... (4)

Subtracting eq.(4) from eq.(3)

112= 28a + 84d

98= 14a + 84d

(-) (-) (-)

14 = 14a

a = 14/14

a =1 ... (5)

Substituting a=1 in eq. (1)

16 = 4a + 12d

16 = 4 + 12d

16 -4 = 12d

12 = 12d

d = 12/12

d= 1 ..... (6)

t11 = a + ( 11-1 ) d

t11 = 1 + 10×1 ..... [from (5) and (6)]

t11 = 1 + 10

t11 = 11