Question 26 of 44intermediate🔧 ApplyShort Answer6 marks

Find the sums given below:

(i)

7 + 10½ + 14 + ... + 84

Answer

2093/2

(ii)

34 + 32 + 30 + ... + 10

Answer

286

(iii)

-5 + (-8) + (-11) + ... + (-230)

Answer

-8930

Explanation

We use the standard formulas for an arithmetic progression (AP). The nth term is given by a_n = a + (n-1)d, and the sum of the first n terms is S_n = n/2 (a + l) where a is the first term, d the common difference, and l the last term. These formulas are illustrated in the provided context (e.g., Example 14). For each series, we first determine a, d, and l, then find n using the nth term formula, and finally compute the sum.