Question

The sum of the second and the fifth term of an AP is 8 and that of the third and the seventh term is 14. Find the eleventh term.
Select one:
a. 19
b. 16
c. 15
d. 17

Answer 1

Answer:

19 is a answer

Explanation:

options a is answer

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Answer 2

The eleventh term is 19

Given:

Sum of the second and fifth terms of AP = 8

Sum of third and seventh term of AP = 14

To find:

The eleventh term.

Solution:

The nth term in an AP is represented as:

an = a1 + ( n-1)d

where a1 is the first term and d is the common difference

Second term = a2 = a1 + ( 2-1) d = a1 + d -- 1

Fifth term = a5 = a1 + ( 5-1) d = a1 + 4d -- 2

Third term = a3 = a1 + ( 3-1) d = a1 + 2d -- 3

Seventh term = a7 = a1 + ( 7-1) d = a1 + 6d -- 4

Now,

a2 + a5 = 8

a1 + d + a1 +4d = 8 ( From eq 1 and 2)

2a1 + 5d = 8 -- 5

Similarly,

a3 + a7 = 14

a1 + 2d + a1 + 6d = 14 ( From eq 1 and 2)

2a1 + 8d = 14 -- 6

Subtracting eq 5 from 6, we will get -

3d = 6

d = 6/3

= 2

From(v),

2a1 + 5×2 =8

2a1  = 8−10

a1 = −1

Therefore, the series is -

= -1, 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21

Answer: The eleventh term is 19

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