In the following questions, two statements (i) and (ii) are given. Choose the valid statement. i. 7 + 10.5 + 14 + ... + 91 = 1125 ii. The number of terms in the progression 8 + 12 + 16 + ... + 124 is 20.

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Neither (i) nor (ii) Explanation: (i) a = 7 d = 10.5 − 7 = 3.5 Last term (l) = 91 l = a + (n − 1)d 91 = 7 + (n − 1)3.5 91 − 7 = (n − 1)3.5 84 = (n − 1)3.5 $\frac{84}{3}$.5 = (n − 1) 24 = n − 1 24 + 1 = n n = 25 Using the formula S_n = n/2(a + l) S_25 = $\frac{25}{2}$(7 + 91) S_25 = $\frac{25}{2}$(98) S25 = 25 $\times$ 49 S25 = 1225 The sum is 1225, but the statement claims it is 1125. Therefore, Statement (i) is false. (ii) a = 8 d = 12 − 8 = 4 Last term (l) = 124 124 = 8 + (n − 1)4 124 − 8 = (n − 1)4 116 = (n − 1)4 $\frac{116}{4}$ = n − 1 29 = n − 1 29 + 1 = n n = 30 The actual number of terms is 30, but the statement claims it is 20. Therefore, Statement (ii) is false.

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