Find the sum of the following APs.
(i) 2, 7, 12,…., to 10 terms
(ii) − 37, − 33, − 29 ,…, to 12 terms

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Solution

(i) $2, 7, 12, \dots \dots, t o 10 t e r m s F o r t h i s A . P ., a = 2 d = a_{2} - a_{1} = 7 - 2 = 5 n = 10 W e k n o w t h a t, S_{n} = \frac{n}{2} [2 a + (n - 1) d] S_{10} = \frac{10}{2} [2 (2) + (10 - 1) \times 5] = 5 [4 + (9) \times (5)] = 5 \times 49 = 245$

(ii) $- 37, - 33, - 29, \dots \dots, t o 12 t e r m s F o r t h i s A . P ., a = - 37 d = a_{2} - a_{1} = (- 33) - (- 37) = - 33 + 37 = 4 n = 12 W e k n o w t h a t, S_{n} = \frac{n}{2} [2 a + (n - 1) d] S_{12} = \frac{12}{2} [2 (- 37) + (12 - 1) \times 4] = 6 [- 74 + 11 \times 4] = 6 [- 74 + 44] = 6 (- 30) = - 180$

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Find the sum of the following APs.

(i) 2, 7, 12 ,…., to 10 terms.

(ii) − 37, − 33, − 29 ,…, to 12 terms

(iii) 0.6, 1.7, 2.8 ,…….., to 100 terms

(iv) ,………, to 11 terms

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