Question

10th term of an arithmetic sequence is 24 and it's 14th term is 36
What is it's common difference?
What is the first term of this sequence?

Answer 1

Answer:

we have given that a10th = 24 and a14th = 36 then

we know that

an = a+(n-1)d

then a10 = a + (10-1)d

24 = a + 9d.....1st equation

and

a14th = a+ (14-1)d

36 = a+13d....2nd equation

from equation 2nd and 1st

a+13d = 36

a+9d = 24

- - -

__________

4d = 12

d = 3

put the value of d in equation 1st

24 = a + 9 (3)

24 = a + 27

24 - 27 = a

a = -3

hence, common difference(d )= 3 and first sequence (a) = -3