Question

the 5th term of an arithmetic sequence is 38 and 9th term is 66 what is it's 30th term what is it's first term and write the common difference​

Answer 1

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25th term is equal to 178.

for calculation see the image above

Answer 2

Given :-

5 th term of an arithmetic sequence is 38 and 9th term is 66

To Find :-

What is it's 30th term what is it's first term and write the common difference​

Solution :-

We know that

nth term = a + (n - 1)d

For 5th term

38 = a + (5 - 1)d

38 = a + 4d (1)

For 9th term

66 = a + (9 - 1)d

66 = a + 8d (2)

Subtracting both

a + 8d - a - 4d = 66 - 38

8d - 4d = 28

4d = 28

d = 28/4

d = 7

From 1

38 = a + 4(7)

38 = a + 28

38 - 28 = a

10 = a

i) 30th term

a_{30} = a + (n - 1)d

a_{30} = 10 + (30 - 1)7

a_{30} = 10 + 29(7)

a_{30} = 10 + 203

a_{30} = 213