Question

The 6th term of an AP is – 10 and 10th term is -26. Determine the sum of the first 20 terms of the AP .

Answer 1

$\huge{\mathcal{\underline{\green{SOLUTION}}}}$

Let a be the First term of the AP

Common Difference = d

${6}^{th} \: term \: = a_6 = a + (6 - 1)d \: = a + 5d$

${10}^{th} \: term \: = a_{10} = a + (10- 1)d \: = a + 9d$

So

$a \: + 5d \: = - 10...........(1)$

$a \: + 9d \: = - 26...........(2)$

Now Equation (1) - Equation (2) gives

$- 4d \: = 16$

$\implies \: d \: = - 4$

From Equation (1)

$a \: = 20 - 10 = 10$

Hence the sum of first 20 terms

$S_{20} = \frac{20}{2} (2a \: + 19d)$

$= 10 \times (2 \times 10 + 19 \times ( - 4))$

$= 10 \times (20 - 76)$

$= - 560$

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Answer 2

Answer:

-560 is answer dear friend