Question

6th term of an arithmetic sequence is 15 and 10th term is 31.FIND
1)First term and common difference
2) 30th term
3)Sum of first 30 terms​

Answer 1

Answer:

1. a = -4 $ d = 4

2. 112

3. 1620

Step-by-step explanation:

Given : 6th term = 15

a + 5d = 15 - (1)

a = 15 - 5d

10th term = 31

a + 9d = 31 - (2)

1.) by putting the value of 1 in 2

15 - 5d + 9d = 31

4d = 16

d = 4

a = 15 - 5d

= 15 - 20

= - 4

2.) by formula an = a + (n-1)d

= -4 + 29× 4

= -4 + 116

= 112

3.) Sn = n/2 (a + l). [An = l]

= 30/2 (-4 + 112)

= 15 * 108

= 1620