Question

The sum of the 1st and 17th terms of an arithmetic
sequence is 40. The sum of its 1st and 18th terms
is 43.
a) What is its common difference?
b) What is the sum of its 7th and 11th terms?
c) Find its 9th term.​

Answer 1

Answer:

a) common difference is 3,

b) 40

c) 20

Step-by-step explanation:

nth term of arithmetic equation is a+(n-1)d

where a is first term and d is common difference

now

=1st term + 17th term = 40

=a+a+(17-1)d=40

=2a+16d=40

-----eq1

2 is common both side so cancel 2 from side we will get

a+8d = 20 ------eq2

which is actually 9th term of the arithmetic sequence.

also given in question,

1st term + 18th term =43

a + a + (18-1)d=43

2a+17d=43 -----eq3

on subtracting eq1 from eq3

we will get

2a+17d=43

2a+16d=40

d=3

HERE OUR A PART IS COMPLETE COMMON DIFFERENCE IS 3.

B)

SUM OF 7TH TERM AND 11TH TERM IS

a+6d+a+10d

=2a+16d

and from eq1 we will get

2a+16d=40.

C) it is already solved in part a when we were trying to find common difference

9th term is

a+8d

From eq2

a+8d= 20.

HOPE IT HELPS

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