Question

The sum of4th and 6th term of an ap is 38 and sum of 5th and 10th teems is 58 find the ap

Answer 1

the answer is in the pic

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Answer 2

Step-by-step explanation:

For an Ap let a be the first term and d be the common difference

according to the first condition

t4+t6 = 38

: . a + (4-1)d + a + (6-1)d = 38 ...[since tn= a+(n-1)d]

: . a+3d+a+5d=38

: . 2a+8d =38 ...(i)

according to second condition

t5+t10= 58

: . a + (5-1)d + a + (10-1)d = 58

: . a + 4d + a + 9d = 58

: . 2a + 13d = 58... (ii)

subtracting equation (i) from (ii) ,we get

2a + 13d = 58

2a + 8d = 38

- - -

5d = 20

: . d= 20/5

= 4

substituting d=4 in equation (i) we get

2a + 8d = 38

2a + 8(4)= 38

2a+ 32= 38

2a = 38-32

: . 2a = 6

: . a = 3