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Sum of First n Natural Numbers

i Find the su...

Question

Question 1 (i)
Find the sum of the following APs.
(i) 2, 7, 12,…., to 10 terms

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Solution

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

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