Question

what is the sum of first 25 terms of an arithmetic sequences 1,6,11
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Answer 1

Given :-

• First term = 1

• Difference = 6 - 1 = 5

• Number of terms = 25

To Find :-

• Sum of first 25 terms of given A.P

Solution :-

$\implies \boxed{ \sf S_n = \frac{n}{2} \bigg [2a + (n - 1)d\bigg]} \\ \\\implies \sf S_n = \frac{25}{2}\bigg [2 \times 1 + (25 - 1)5\bigg] \\ \\\implies \sf S_n = \frac{25}{2} \bigg[2 + (24)5\bigg] \\ \\\implies \sf S_n = \frac{25}{2} \bigg[2 + 120\bigg] \\ \\\implies \sf S_n = \frac{25}{2} \times 122 \\ \\\implies \sf S_n = 25 \times 61 \\ \\ \implies \underline{ \boxed{ \sf S_n = 1525}}$