Question

the first term of an arithmetic sequence is 10 and the sum of the first five terms is 250,find the sequence​

Answer 1

Answer:

The  sequence  is:

10, 30, 50, 70, 90.....................

Step-by-step explanation:

We have,

First term (a) = 10

Common difference (d) = ?

Sum of first 5 terms ($S_{5}$) = 250

or, $\frac{n}{2} [{2a+(n-1)d}] = 250$

or, $\frac{5}{2} [2*10 + 4d]=250$

or, $\frac{5}{2} * 4[5+d]=250$

or, 10(5 + d) =250

or, 5 + d = 25

∴ d = 20

Now,

2nd term = a + d = 10 + 20 = 30

3rd term = a + 2d = 10 + 2*20 = 10 + 40 = 50

4th term = a + 3d = 10 + 3*20 = 10 + 60 = 70

5th term = a + 4d = 10 + 4*20 = 10 + 80 = 90