Question

if t3+t8=7 & t7 +t14=-3 find t10

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Answer 1

Answer:

Given : t3 + t8 =7

t7+t14 = -3

To find: t10

Solution:

t3 + t8 =7............... (1)

We know that ,

tn = a + ( n-1) d

From this formula we simply (1),

a+ (3-1) d + a+ (8-1)d = 7

a+2d + a+7d = 7

2a + 9d = 7 ........... (2)

Similarly,

t7 + t14 = -3 ..............(3)

By simplifying (3) , we get

a+ ( 7-1)d + a+ (14-1)d = -3

a+6d + a+13d = -3

2a + 19d = -3.............(4)

Subtracting (3) from (4) , we get

2a + 19d = -3 .........(4)

2a + 9d = 7 ......... (3)

- - -

_____________

10d = -10

d = -10/10 =-1

Substituting the value of d in (3) , we get

2a + 9 (-1) = 7

2a -9 =7

2a= 7+9

2a = 16

a = 16 /2 =8

Now ,

tn = a+(n-1) d ....... ( formula)

t10 = 8 + (10-1) (-1)

= 8 + 9(-1)

= 8 -9

= -1