Question

Let 3, 6, 9, 12 ....... upto 78 terms and 5, 9, 13, 17 ...... upto 59 be two series. Then, the sum of the terms common to both the series is equal to ______.

विकल्प

• 2220

• 2221

• 2222

• 2223

Answer 1

Let 3, 6, 9, 12 ....... upto 78 terms and 5, 9, 13, 17 ...... upto 59 be two series. Then, the sum of the terms common to both the series is equal to 2223.

Explanation:

Given: 3, 6, 9, 12, 15, 17, ......up to 78 terms

Now, last term of first series t₇₈ = 3 + 77 × 3 = 234

And last term of second series t₅₉ = 5 + 58 × 4 = 237

Now, common difference of common terms = LCM {3, 4} = 12

∴ First common term is 9 and last common term is 225.

So, series will be 9, 21, 33, ......, 225

∵ t_n = 225

⇒ 9 + (n – 1)12 = 225

⇒ n = 19

∴ Sum of common on terms = S_n = `19/2(9 + 225)` = 2223