Question

37. Find the sum of first 22 terms of an AP in which third term is 7 and seventh term is 2 more than thrice of its third term.​

Answer 1

Question:-

Find the sum of first 22 terms of an AP in which third term is 7 and seventh term is 2 more than thrice of its third term.

Answer:-

Given:

• a3 = 7
• a7 = 3a3 + 2

To find:-

• Sum of first 22 sums.

________________

• a + 2d = 7
• a + 6d = 3 (a+2d) + 2
• Here a is -1
• a = -1 , d = 4

------------------------

➦ Sn = n/2 [2a + ( n-1 ) d]

➦ Sn = 22/2 [ 2(-1) + (22-1) x 4]

➦ Sn = 11 [ -2 + 44 ]

➦ Sn = 242

So sum of first 22 terms is 242.