Question

In an AP, Sn=3n+5 then, the value of ‘d’ is:

A) 3

B) 5

C) -5

D) 8​

Answer 1

Given :- In an AP, Sn=3n+5 then, the value of ‘d’ is:

A) 3

B) 5

C) -5

D) 8

Solution :-

→ Sn = 3n + 5

so,

at n = 1,

→ S1 = 3*1 + 5 = 3 + 5 = 8

at n = 2

→ S2 = 3*2 + 5 = 11

Let first term of given AP is a and common difference is d .

so,

→ S1 = a1 = 8

→ S2 = a1 + a2

→ S2 = a1 + (a1 + d)

then,

→ a1 + (a1 + d) = 11

→ 8 + 8 + d = 11

→ 16 + d = 11

→ d = 11 - 16

→ d = (-5) (C) (Ans.)

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Answer 2

SOLUTION

TO CHOOSE THE CORRECT OPTION

$\sf{In \: an \: AP \: \: S_n = 3n + 5 \: \: then \: the \: value \: of \: d \: is }$

A) 3

B) 5

C) -5

D) 8

EVALUATION

Here it is given that

$\sf{In \: an \: AP \: \: S_n = 3n + 5 }$

Now

$\sf{S_n = Sum \: of \: first \: n \: terms \: of \: the \: AP }$

Putting n = 1 we get sum of first one term of the AP

Sum of first one term of the AP

= First term

= ( 3 × 1 ) + 5

= 3 + 5

= 8

Putting n = 2 we get sum of first two term of the AP

Sum of first term term of the AP

= First term + Second term

= ( 3 × 2 ) + 5

= 6 + 5

= 11

From above we get

First term = 8

Second Term = 11 - 8 = 3

Common Difference = d = 3 - 8 = - 5

∴ d = - 5

FINAL ANSWER

Hence the correct option is C) - 5

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