#### A sequence a_1, a_2, a_3, … is defined by a_1 = 3, a_{n+1} = 3a_n -5 , n ≥ 1.

Calculate the value of \sum_{r=1}^{5} a_r

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Calculate the value of \sum_{r=1}^{5} a_r

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Step 1: Examine the summation

\sum_{r=1}^{5} a_r = a_1 + a_2 + a_3 + a_4 + a_5

Step 2: Make sure that the given set of numbers arranged in some particular order. Because the question says that the set of numbers in sequence.

Step 3: Explore the given rule

EXAMPLE: x_{n+1} = ax_n - 3

Succeeding term = a (preceding term) - 3

Step 4: According to the given rule substitute the (n)values.

[NOTE: To find the twenty-first term, replace n by 21. based up on the rule it(n) may change to lower value or higher value]

EXAMPLE: For an attempt to find the x_2 substitute n=1 in the given rule

x_{n+1} = ax_n - 3

x_2 = ax_1 - 3

Substitute the values x_1 [ take x_1 = 1 since n >1), Some times it mention

in the question]

x_ 2 = a(1) - 3

x_2 = a - 3

Step 5: Simplify further

(Apply the BODMAS rules)

Step 6: Repeat the same steps to calculate all the values of a_1, a_2, a_3, a_4, a_5 and add them