Question

2.
There are 20 terms in an arithmetic sequence. Sum of
the first and last terms is 88.
(a) What is the sum of the 2nd and 19th terms?
(b) If the 10th term is 42, what is the 11th term? What
is the common difference of the sequence ?
(d) What is the first term ?​

Answer 1

Given :

• n = 20
• Sum of first and last term = 88
• 10th term = 42

To find :

• Sum of 2nd and 19th term
• 11th term
• Common difference (d)
• First term (a)

Solution :

Sum of first and last term = 88

First term = a

last term (20th term) = a + 19d

$\therefore$ a + a + 19d = 88

2a + 19d = 88

a) Sum of 2nd and 19th term = (a + d) + (a + 18d)

= a + d + a + 18d

= 2a + 19d

= 88

b) Sum of 10th and 11th terms = ( a +9d) + (a + 10d)

= a + 9d + a + 10 d

= 2a + 19d

= 88

Given : 10th term = 42

42 + a + 10d = 88

a + 10d = 88 - 42

a + 10 d (11th term) = 46

Common Difference = 11th term - 10th term

= 46 - 42

= 4

c) a + 10d = 46

a + 10×4 = 46

a + 40 = 46

a = 46 - 40

a = 6