Question

In an A.P 4th and 8th term are 13 and 29 respectively. Calculate the sum of first 10 numbers ​

Answer 1

Answer:

the sum of the first 10 numbers is 190.

Answer 2

= 190

Step-by-step explanation:

Given:

4th term = 13

8th term = 29

Find S10 =?

An = a +(n - 1)d

4th term = 13 , n=4

13 = a + (4 - 1)d

13 = a + 3d...................eq1

8th term = 29 , n=8

29 = a + (8 - 1)d

29 = a + 7d..................eq2

From eq2 - eq1

16 = 4d

16/4 = d

4 = d

Put d=4 in eq 1

13 = a + 3d

13 = a + 3(4)

13 = a +12

13-12 = a

1 = a

So, Sn = n/2[2a + (n-1)d]

where, n=10

S10 = 10/2[2x1 + (10-1)4]

S10 = 5[2 + 9(4)]

      = 5[2+36]

      = 190

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