Question

If the 3rd and 6th term of an Ap are 7 and 13 respectively find out the sum of first 20 terms of the series

Answer 1

SOLUTION

GIVEN

The 3rd and 6th term of an Ap are 7 and 13 respectively

TO DETERMINE

The sum of first 20 terms of the series

EVALUATION

Let the first term = a and common difference = d for the given Arithmetic progression (AP)

Then

3rd term = a + ( 3 - 1 ) d = a + 2d

6th term = a + ( 6 - 1 ) d = a + 5d

So by the given condition

$\sf{a + 2d = 7 \: \: \: .......(1)}$

$\sf{a + 5d = 13 \: \: \: .......(2)}$

Now Equation (2) - Equation (1) gives

$\sf{3d = 6}$

$\implies \sf{d = 2}$

From Equation (1) we get

$\sf{a = 7 - (2 \times 2)}$

$\implies \sf{a = 3}$

Hence the required sum of first 20 terms

$\displaystyle \sf{ = \frac{20}{2} \times \bigg[ \: 2a + (20 - 1)d \bigg]}$

$\displaystyle \sf{ = 10 \times \bigg[ \: 2a + 19d \bigg]}$

$\displaystyle \sf{ = 10 \times \bigg[ (2 \times 3) + (19 \times 2) \bigg]}$

$\displaystyle \sf{ = 10 \times (6 + 38)}$

$= 10 \times 44$

$\sf{ = 440}$

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