Correct Answer - Option 3 : 1032
Given:
The first term, a = T5 – 32
The common difference, d = 4a/21
Formula used:
Tn = a + (n – 1) d
Sn = n/2 × [2a + (n – 1) d]
Where, a = first term, n = number of terms and d = common difference
Calculation:
T5 = a + (5 – 1) d
⇒ T5 = a + 4d
According to question-
⇒ a + 4d – 32 = a
⇒ 4d = 32
⇒ d = 32/4
⇒ d = 8
Now, d = 4a/21
⇒ 8 = 4a/21
⇒ a = 42
Therefore, S12 = 12/2 × [2(42) + (12 – 1) 8]
⇒ S12 = 6 × [84 + 88]
⇒ S12 = 6 × 172
∴ S12 = 1032