Question

The sum of first n term of an AP is 210 and sum of its first (n-1) terms is 171 if the first term 3,then write the AP.

Answer 1

Step-by-step explanation:

To find the AP if the sum of first n terms of arithmetic progression is 210 and sum of its first (n-1) terms is 171. If the first term is 3 . As we know that if AP has n terms,then after removing (n-1) terms,we are left with the last term. so, arithmetic progression is 3,7,11,15...

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Answer 2

$\Large{\textbf{\underline{\underline{According\;to\;the\;Question}}}}$

Here,

Last term,

= 270 - 171

= 39

Also

First term,

a = 3

Using Formula we have,

S(n) = n/2{a + l}

210 = n/2{3 + 39}

210 = n/2 × 42

420 = 42n

420/42 = n

n = 10

Also,

We know that,

S(n) = n/2[2a + (n - 1)d]

210 = 10/2[2 × 3 + (10 - 1)d]

210 = 5[6 + 9d]

210/5 = 6 + 9d

42 = 6 + 9d

42 - 6 = 9d

36 = 9d

36/9 = d

d = 4

Therefore,

A.P = 3, 7, 11, 15, ......... , 39