Question

What is the sum of 25 terms of an arithmetic progression (ap) whose first term is 5 and common difference is 7/4?

Answer 1

SOLUTION

TO DETERMINE

The sum of 25 terms of an arithmetic progression (ap) whose first term is 5 and common difference is 7/4

EVALUATION

Here it is given that

First term = a = 5

$\displaystyle \sf{Common \: Difference = d = \frac{7}{4} }$

Hence the required sum of 25 terms

$\displaystyle \sf{ = \frac{25}{2} \bigg[ \: 2 \times 5 + (25 - 1) \times \frac{7}{4} \bigg] }$

$\displaystyle \sf{ = \frac{25}{2} \bigg[10 + 24 \times \frac{7}{4} \bigg] }$

$\displaystyle \sf{ = \frac{25}{2} \bigg[10 +4 2\bigg] }$

$\displaystyle \sf{ = \frac{25}{2} \times 52 }$

$\displaystyle \sf{ = 25 \times 26 }$

$= 650$

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