Question

If the sum of first four terms of an A.P. is 40 and that of
fourteen terms is 280, find the sum of first n terms.
(CBSE 2016)​

Answer 1

Answer:

Brainly.in

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Anjali2820

nikitajha400

nikitajha400

21.06.2017

Math

Secondary School

+5 pts

Answered

If the sum of first 4 terms of an AP is 40 and that of first 14 the is 280, find the sum of first n term

Answers

The Brain

Parisakura98pari Ace

Sn = sum of n terms of an A.P. = n/2 [ 2a + (n-1)d]

A/Q

S₄ = 40 = 4/2 [2a + 3d] = 2a + 3d = 20 ...........(1)

and

S₁₄ = 280 = 14/2 [2a + 13d] = 2a + 13d = 40 .........(2)

solving (1) and (2)

gives a = 7 and d= 2

so Sn = n/2[ 2(7) + (n-1)2] = 7n + n² - n = n² + 6n

I hope it helps you

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Answer 2

Answer:

Step-by-step explanation:

s4=40

s14=280

s4=4/2[2a+[4-1]d]

40/2 = [2a+3d]

20=2a+3d                          .......1

s14= 14/2 [2a+[14-1]d]

280=7[2a+13d]

280/7=2a+13d

40=2a+13d                        ........2

eq.2-eq.1

40=2a+13d

20=2a+3d

[-]   [-]   [-]

________

20=10d

d=2

sub. d=2 in eq.1

20=2a+3 x 2

20-6=2a

14=2a

a=7

the sum of n terms = n/2[2a+[n-1]d]

                               = n/2 x[14+2n-2]

                               = n/2 [12+2n]

                               n/2[2[6+n]

                            =n[6+n]

                                6n+n^2

therefore the sum of n terms is 6n+n^2