Question

In a A.P. t17 is 34. Find out S33​

Answer 1

SOLUTION

GIVEN

In an AP

$\sf{ t_{17} = 34\: }$

TO DETERMINE

$\sf{S_{33}}$

CONCEPT TO BE IMPLEMENTED

If in an arithmetic progression

First term = a and Common difference = d

Then

1. The nth term of the progression is

$\sf{t_n = a + (n - 1)d}$

2. The sum of the first n terms

$\displaystyle \sf{S_n = \frac{n}{2} \bigg[2a + (n - 1)d \bigg] }$

EVALUATION

Here it is given that for an arithmetic progression

$\sf{ t_{17} = 34\: }$

Let first term = a and common difference = d

$\sf{ t_{17} = 34\: }$

$\implies \sf{a + (17 - 1)d = 34 \: }$

$\implies \sf{a + 16d = 34 \: } \: \: \: ......(1)$

Hence

$\displaystyle \sf{S_{33} = \frac{33}{2} \bigg[2a + (33 - 1)d \bigg] }$

$\displaystyle \sf{= \frac{33}{2} \bigg[2a + 32d \bigg] }$

$\displaystyle \sf{= 33 \bigg[a + 16d \bigg] }$

$\sf{ = 33 \times 34\: } \: \: (\: using \: \: eqn. \: 1)$

$= \sf{1122}$

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