Question

10. The sum of 2nd and 30" term of an arithmetic sequence is 50
a. What is the sum of 1 and 31" terms?
b. What is the sum of 5th and 27th terms? c.
What is the 16th term?
d. What is the sum of first 31 terms? ​

Answer 1

Step-by-step explanation:

in an arithmetic sequence the terms are given as -

1, 2 3 4

a, a + d, a + 2d, a + 3d

the 2nd term is a + d

and 30th term is a + 29d

sum of 2nd and 30th term is given as 50

a + d + a + 29d = 50

2a + 30d = 50 equ 1

a) 1st + 31st

sum of first term and 31st term

a + a + 30d

2a + 30d = 50 (same as equ 1)

b)5th + 27th

a + 4d + a + 26d

2a + 30d = 50 (same as equ 1)

c) 16th term = a + 15d

2a + 30d = 50

2 (a + 15d) = 50

a + 15d = 50/2

a + 15d = 25

d) sum of first 31 terms

$= \frac{n}{2} (2a + (n - 1)d) \\ = \frac{31}{2} (2a + (31 - 1)d) \\ = \frac{31}{2} (2a + 30d) \\ = \frac{31}{2} \times 50 \: \: \: \: (as \: 2a + 30d = 50) \\ = 31 \times 25 \\ = 775$

Hope you get your answer