Maths / Arithmetic Progression / Sum of N Terms When First Term, Last Term and Number of Terms are Given

QUESTION

Find the sum of the series: 7 + 15 + 23 + 31 + 39 + 47 + ……….. + 255

 OPTIONS A. 3192 B. 4099 C. 4192 D. 4455
Right Option : C

EXPLANATION
Explain TypeExplanation Content
Text

First term of the given arithmetic series = 7

Second term of the given arithmetic series = 15

Third term of the given arithmetic series = 23

Fourth term of the given arithmetic series = 31

Fifth term of the given arithmetic series = 39

Now, Second term - First term = 15 - 7 = 8

Third term - Second term = 23 - 15 = 8

Fourth term - Third term = 31 - 23 = 8

Therefore, the given sequence is ann arithmetic series with the common difference 8.

Let there be n terms in the given arithmetic series. Then

ann = 255

⇒ a + (n - 1)d = 255

⇒ 7 + (n - 1) × 8 = 255

⇒ 7 + 8n - 8 = 255

⇒ 8n - 1 = 255

⇒ 8n = 256

⇒ n = 32

Therefore, the required sum of the series = 322322[2 ∙ 7 + (32 - 1) ∙ 8]

= 16 [14 + 31 ∙ 8]

= 16 [14 + 248]

= 16 × 262

= 4192

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