Let a1, a2, ldots, a10 be an AP with common difference -3 and b1, b2, ldots ., b10 be a GP with common ratio 2 . Let c k = a k + b k , k =1,2, ldots, 10 . If c 2=12 and c3=13, then displaystyle∑ k =110 C k is equal to

Question

Let a1, a2, ldots, a10 be an AP with common difference -3 and b1, b2, ldots ., b10 be a GP with common ratio 2 . Let c k = a k + b k , k =1,2, ldots, 10 . If c 2=12 and c3=13, then displaystyle∑ k =110 C k is equal to (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

c2=a2+b2 =a1-3+2 b1=12 a1+2 b1=15 ...(1) c3=a3+b3 =a1-6+4 b1=13 a1+4 b1=19 ...(2) from (1) (2) b1=2, a1=11 displaystyle∑ k =110 c k = displaystyle∑ k =110( a k + b k )= displaystyle∑ k =110 a k + displaystyle∑ k =110 b k =(10/2)(2 × 11+9 ×(-3))+(2(210-1)/2-1) =5(22-27)+2(1023) =2046-25=2021

Q. Let a1​,a2​,…,a10​ be an AP with common difference −3 and b1​,b2​,….,b10​ be a GP with common ratio 2 . Let ck​=ak​+bk​,k=1,2,…,10. If c2​=12 and c3​=13, then k=1∑10​Ck​ is equal to

Q. Let $a_{1}, a_{2}, \dots, a_{10}$ be an $A P$ 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 $k = 1 \sum 10 C_{k}$ is equal to