Statement 1 : The sum of the first 30 terms of the sequence…

Maths Sequence and Series ( Progressions ) Summation of Series Single Correct MCQ

Published on: August 14, 2026

Statement 1 : The sum of the first 30 terms of the sequence 1,2,4,7,11,16, 22,....is 4520

Statement 2 : If the successive differences of the terms of a sequence form an A.P., then general term of sequence is of the form an 2 + bn + c.

STATEMENT-1 is true, STATEMENT- 2 is true and STATEMENT- 2 is correct explanation for
STATEMENT- 1

STATEMENT-1 is true, STATEMENT- 2 is true and STATEMENT- 2 is not correct explanation for STATEMENT- 1

STATEMENT-1 is true, STATEMENT- 2 is false

STATEMENT- 1 is false, STATEMENT- 2 is true

Text Solution

Verified by Experts

The correct answer is:

S = 1 + 2 + 4 + 7 + 11 + 16...............T n ...(i)

S = 1 + 2 + 4 + 7 + 11 ...............T n ...(ii)

(i) – (ii) we get

O = 1+(1+2+3+4+5............(n–1) term) – T n ⇒

∴ General term = T n = an 2 + bn + c here a = 1/2 , b= –1/2 , c = 1

S n = = – + n

S 30 = – + 30 = 4727.5 – 232.5 + 30 = 4525

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