Question

.find the sum of 25 term of an A.P having common difference 6 and 18 term is 110
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Answer 1

Answer:

answer is 200

Step-by-step explanation:

d=6

a18=110

a+17d=110

a+17*6=110

a+102=110

a=110-102

a=8

S25=n/2(2a+(n-1)d)

s25=25/2(2×8+24×6)

=25/2×160

S25=200

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Answer 2

The sum of 25 term of the given A.P series is 2000.

Step-by-step explanation:

The common difference, d=6

Then, the 18th term is 110,  $a_{18} =110$

As we know that, the sum of first term and the nth term will give (n+1)th term.

Therefore,

                                               $a_{18}$ = a+17d =110

Then substitute the value of d= 6,

                                             a + (17 $\times$ 6) =110

                                               a + 102 = 110

                                               a= 110 - 102

                                                   a = 8 .

Then, the first term is 8.

As we know the formula, that is

                                        $S_n$ = $\frac{n}{2} (2a+(n-1)d)$

                                      $S_{25} = \frac{25}{2} (2a+(25-1)d)$

                                    $S_{25} = \frac{25}{2} ((2\times 8} + (24 \times 6))$

                                                = $\frac{25}{2} \times 160$

                                                 = 25 $\times$ 80

                                               = 2000.

                                              $S_{25} =2000.$

Therefore, the sum of 25 term of the given A.P series is 2000.

To know more:

If sum of first 6 terms of an A.P is 36 and that of the first 16 terms is 256.Find the sum of first 10 terms.

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