Mathematics

Problem

Let

a_1, a_2, \dots, a_{10}

be an AP with common difference -3 and

b_1, b_2, \dots, b_{10}

be a GP with common ratio 2. Let

c_k = a_k + b_k, k = 1, 2, \dots, 10

. If

c_2 = 12

and

c_3 = 13

, then

\sum_{k=1}^{10} c_k

is equal to ____.