(c) if the corresponding terms of two arithmetic sequences are added, is the resulting sequence arithmetic?

To determine whether the corresponding terms of 2 arithmetic sequence's added will give new arithmetic sequence or not, Let' take 2 Arithmetic sequences.

In one first term is a1 and common difference is d1, in the other first term is a2 and common difference is d2.

Now nth term for first sequence = a1+(n-1) d1

  nth term for second sequence = a2+(n-1) d2

Now add the 2 terms: a1+(n-1)d1 +a2 +(n-1)d2

                                   = a1+a2 + (n-1)(d1+d2)

This is again new arithmetic sequence with first term a1+a2 and common difference d1+d2.

Hence if we add corresponding terms of 2 arithmetic sequence, we will again get an arithmetic sequence.

17.08

correct me if i am wrong.

answer: - (a)

(b) 88 seats

step-by-step explanation:

given: in an auditorium, there are 22 seats in the first row and 28 seats in the second row.

thus first term=

second term=

the number of seats in a row continues to increase by 6 with each additional row.

⇒d= 6

a) given formula :

b)   let the number of seats (n) = 12

substitute n=12 in the explicit rule formed in (a)

∴there are 88 seats in 12 rows.